Police were called after the 34-year-old was seriously injured in the incident in the Wallace Court area of the city just before 11pm on Saturday.
He was taken to Ninewells Hospital in Dundee for treatment but died in the early hours of Sunday.
A 19-year-old man has been detained and is assisting officers in connection with the incident.
Detective Inspector Brian Geddes of Police Scotland’s Major Investigation Team, who is leading inquiries, said: “I would like to reassure the local community that this was a contained and isolated incident and at no point was there any threat posed to any other member of the public.
“Officers will remain in the area while further enquiries are carried out, and I would like to thank people who live nearby for their patience meantime.
“Our thoughts are with the family and friends of the man who died at this very sad time.”