The two men, who have not been named, were photographed dressed in cardboard painted in Mandarin characters, reading ‘New Year’ ‘suck my chopsticks’ and ‘I love hockey’.
One of the revellers could be seen clutching a full bottle of Buckfast, while the other held a beer can.
In the lead up to the party, organisers posted on the Facebook event warning guests there would be “zero tolerance for people taking the piss with the theme”, adding “the last thing we want is to cause offence”.
However, the photograph circulated online and was described by the President of the University of Edinburgh Hong Kong International Society as an incident of “racial discrimination and white privilege”.
The President of the Edinburgh University Hong Kong International Society, Robyn Ma, said: “The Chinese New Year themed party was not a celebration of the New Year.
“It was a racist-themed party and a flagrant act of disrespect towards Chinese culture.
“Instead of celebrating this tradition, they were celebrating white privilege.
“Wearing ‘yellow face’ and carrying signs with texts mocking our culture is incredibly offensive.
“This is not a celebration of our culture at all.
“I’d like to believe that this wasn’t an intentional act of racial discrimination, but rather of ignorance.
“What happened is not a reflection of all students at Edinburgh but I believe it is important to highlight the fact that these instances of white privilege continue to exist and are unacceptable.”
One of the students, who spoke on condition of anonymity, denied that there was a racist element to the costumes, and told student publication The Tab the pair had dressed up as chopsticks.
The lad said: “It is extremely upsetting to both of us how these costumes have come across following the party given our genuine intention was to dress up as chopsticks.
“Whilst we understand and sincerely apologise for any offence caused by these photos, we would like to make it very clear that any allegations of us intending to dress as anything else are a total misrepresentation of us as individuals and of our intentions at that party.”
The party was held in February and was attended by around 75 people.
The Facebook post inviting guests suggested attendees dress in red and gold colours, Chinese blossom patterns, or as zodiac signs and animals including pigs, tigers, rabbits and dragons.
Another guest who attended the party said: “The party was themed for Chinese New Year, and in this context two people came together dressed as two chopsticks.
“They put cardboard boxes around their bodies and on their heads, and put beige paint on their exposed skin.
“In some of the photos taken at the end of the night, the lighting and faded paint had lightened the beige colour of the paint on their skin.
“When they and the hosts realised that the photos had caused offence they immediately took them off Facebook.
“In no way was the outfit meant to be ‘yellow-face’.
“I am confident that no one who saw the costumes in person considered that it was.”
Sign up to our newsletter: enter your email in the box at the top of this article to get daily updates straight to your inbox.