Nolan, a loosehead prop, suffered the break while playing against Alhambra-Union for his Harbour club side on Saturday.
Coupled with Keith Cameron damaging his shoulder in a club game on May 30, Otago's propping ranks are looking thin, with the kick-off of the ITM Cup less than two months away.
Nolan was expected to be the starting loosehead prop for Otago this year, after making 11 appearances for the side last season.
The 26-year-old had moved to Australia at the end of last year after he failed to pick up a Super 14 contract but was enticed back to the union last month and had played a couple of games for Harbour.
But after breaking his wrist he may struggle to make the first game for Otago, with the side due to play Counties-Manukau in its opening game of the ITM Cup on July 31.
Otago coach Phil Mooney said Nolan was likely to be out of the game for between eight and 12 weeks but he was hopeful of getting him back by the end of next month.
Cameron dislocated his left shoulder while playing for Dunedin against Harbour and was initially hopeful of being back playing within a month.
It had been put back into its socket straight after the match.
But Cameron is due to see a specialist this week to see how bad the damage is and when he will get back on the paddock.
Otago is not deep in propping options, with Sam Hibbard getting back into form for University A after a slow start to the season, while other options include Pieter van der Merwe and veteran Kees Meeuws.
Halfback Sean Romans is also still on the injured list, slowly coming back from a hamstring injury.
Romans tore his hamstring after falling awkwardly in a tackle while playing for University A in April and was on crutches for a time.
Mooney said he was now doing strength work to get back up to speed.
Mooney was hopeful Romans would be able to get in some club play before the end of the club season, as he continues his rehabilitation.
Otago first five-eighth Chris Noakes is overseas and will not return until later this month.
On the positive side, outside back Ryan Shortland played his first club game for Taieri last Saturday, returning from a knee injury.
Winger Chris Small, who signed from Canterbury last week, was unlikely to arrive before the end of the club season as he was studying engineering at the University of Canterbury and had study commitments into next month.
The club final is due to be played on July 17.
