The depiction of Scandinavians in popular media has been so consistently stereotypical that most people can conjure an image of the ideal Dane, Swede, or Norwegian.
The average Scandinavian is tall, blonde, and blue-eyed in this collective imagination. How then to account for seeming anomalies like “Asian eyes.”
A small fraction of Scandinavians have eyes that people characteristically associate with people of East Asian descent because of their high incidence among East Asian people.
These features are sometimes described as Asian eyes.
This article will clarify the matter in greater detail, explaining the incidence of characteristically Asian features in some Scandinavians and the features that can be found in more typically Scandinavian faces.
Also see Why Are Scandinavian Women So Beautiful? for more about the appearance of Northern Europeans.
What Do People Mean by Asian Eyes?
What people mean by Asian eyes are dark brown eyes with epicanthic folds (folds on the upper eyelid along the inside corner of the eye).
These features are common among people of East Asian descent. Their occurrence in Scandinavians is likely due to traces of Sami, Inuit, or East Asian ancestry.
Epicanthic folds are the folds of skin on the upper eyelid where it meets the inner corner of the eyes. They tend to give the eyes a narrower, slanted appearance.
Epicanthic folds are most commonly present in high concentrations in adults of East Asian descent.
Similarly, while brown is the most common eye color in the world, dark brown eyes, in particular, are especially common in East and South-East Asia. 
Taken together, dark brown eyes with epicanthic folds have come to be strongly associated with East Asian peoples.
This historical association explains the assumption that some Scandinavians have Asian eyes.
However, it is important to remember that many differences exist — in facial features and other qualities — between East Asians and Scandinavians as groups and that neither is entirely uniform.
Besides, essentializing people based on physiognomic characteristics can be inaccurate and ethically problematic.
On the one hand, most Scandinavians do not have dark brown eyes with epicanthic folds.
The few who do will likely have inherited these traits via Sami, Inuit, or Asian ancestry.   
The Sami are Finno-Ugric-speakers whose historical homelands encompass parts of Sweden and Norway and areas outside of Scandinavia.
Inevitably, Sami and other Scandinavian populations have mixed to some degree over the years.
Similarly, the Inuit are a culturally similar indIgenous people whose homelands span the Arctic and sub-Arctic regions of Alaska, Canada, and Greenland.
Due to Denmark’s long colonial association with Greenland, there has been some mixing of Danish and Inuit populations over the years.
Thus, the characteristic epicanthic eyes of some Scandinavians can be traced to the mixing of populations within the Scandinavian region over many thousands of years.
At the same time, categorizing anything, let alone aspects of human physiognomy, as ‘Asian’ is highly problematic considering that, at over 4.5 billion, the population of Asia includes almost 60% of all humans alive today.
Moreover, using physical features to define racial characteristics has a dark history. 
In the past, the characterization of epicanthic folds as a peculiarly Asian characteristic has been used to reinforce ideas of racial superiority.
For instance, Down Syndrome was initially described as “Mongolism” because slanted eyes and epicanthic folds in infants were a few of the many indicators of the disease.
Thinking using such lazy tools can be a slippery slope to acting based on them. In the worst cases, it can set the stage for racist atrocities.
Also, see Why Do Some Icelandic People Look Asian? to learn more.
What Color Eyes Do Scandinavians Have?
Scandinavians have eyes of all colors found among human populations.
Although a majority of people in Norway, Denmark, and Sweden have blue eyes, many others have brown, green, or gray eyes.
The stereotype of blue-eyed Scandinavians is based on the fact that a majority of Scandinavians really do have blue eyes.
As per recent studies, the population with blue eyes among the different Scandinavian countries is the highest in Sweden (78%), followed by Denmark (59.6%), and Norway (55%). 
The variation in eye color in Scandinavians is not unusual considering the history of migrations into the region over thousands of years.
While gaining insights into these deep historical events is challenging, genetic studies conducted in recent decades provide some idea of the movements of human populations over millennia.
According to these studies, the first Scandinavians–hunter-gatherers migrating from the south 14,000 years ago–were predominantly dark-skinned and blue-eyed.
Later, they were joined by other hunter-gatherers, this time from the east, who primarily had light skin and dark eyes.
Over the centuries, these two populations intermingled, giving rise to greater diversity in the appearance of the region’s population.
In fact, the mixing of populations in Scandinavia at the time produced a greater diversity than has been found in the rest of Europe for the same period.
Later, many other waves of migration into the Scandinavian peninsula occurred over thousands of years, further enriching this diversity.
The first farmers reached Scandinavia from Anatolia and Syria 6000 years ago. Another thousand or so years later, herders from the Russian steppes arrived.
And migration into the region continues to this day, including from East Asian countries.
This is why, today, the population in the Scandinavian countries is only about 65-80% Scandinavian in terms of its DNA.
In fact, there are very few “pure” racial populations anywhere in the world anymore.
Also, see Why Do Scandinavians Tan So Well? to learn more.
What Are Typical Scandinavian Facial Features?
Typical Scandinavian facial features include:
- Blonde or light brown hair
- Pale skin
- Blue eyes
- Straight, narrow noses
- Pointed chins
- Broad foreheads
- Small cheeks
Once again, all the caveats laid out in the earlier two sections apply here too.
While most or many Scandinavians might have the features listed above, not everyone will have these exact features.
Many Scandinavians have dark hair and eyes, for instance, and generalizing or expecting uniformity can be both inaccurate and ethically fraught.
A small subset of Scandinavians have eyes that may be erroneously labeled Asian eyes based on physiognomic features most common among East Asian populations.