It happened at about 20:00 BST at Rafters bar and restaurant in Northland Road area on Wednesday.
He was treated for a hand injury at Altnagelvin Hospital and discharged a short time later.  It is understood the wedding involved members of the travelling community.
A man was later arrested by Irish police in County Donegal.
SDLP councillor John Boyle said a shotgun was used.
"A weapon was discharged, I believe that weapon was a shotgun," he said.
"At around 8.30pm, police told me, they received a report of an incident relating to some type of altercation at the Rafters bar and restaurant on the Northland Road, Ballymagroarty area," said Mr Boyle.
"It's always very worrying when you hear about weapons being produced whether it be at a wedding, on the street or in someone's home, there is always the very real potential for death or serious injury."
A man in his 30s has been injured in a shooting at a wedding reception in Londonderry.