It happened in Bedford Street between 03:40 GMT and 04:00 GMT last Sunday.
The man, who is a foreign national, was taken to hospital but his injuries are not believed to be life threatening.
Police have said the attacker is in his early 30s, of slim build and around 5'11" tall.
He was wearing dark clothing and was armed with what police have said was a sharp object.
Police are appealing for witnesses.
A man in his 40s has been assaulted in Belfast city centre in what police have said was a racially motivated hate crime.