The incident happened on Alfred Street near its junction with Sussex Place shortly before 02:00 BST on Sunday.
The victim, who is in his 30s, was taken to hospital for treatment to a deep cut to his face.
The suspect, who is described as being about 5'8" (172cm) tall and of stocky build, made off towards Ormeau Avenue.
Police have appealed for anyone who was in the area at the time of the attack to contact them on the non-emergency number 101.
A man has been stabbed in the face in an attack in Belfast city centre.