The Trotters centre-back came off during Sunday's 2-2 draw with West Brom and scans have since revealed the extent of the injury.
The news will come as a blow to manager Owen Coyle prior to the vital showdown with Stoke on Sunday which Bolton must win to stand any chance of Premier League survival.
Coyle currently also has injury concerns over Gretar Steinsson, Nigel Reo-Coker and Martin Petrov ahead of the clash with the Potters.
Before the news on Wheater broke, Coyle told Bolton News: “Nigel has played through an injury but I thought he did well.
“We’ll have to take stock at the start of the week and see where we go from there. Injuries we have picked up this year have been beyond belief.
“We have got to take the slap in the teeth - which it undoubtedly is - and try and get a team out on the pitch.
“We can make it right but it will need a big performance at Stoke.”
Bolton have had to cope for extended periods of time without key midfield pair Stuart Holden and Lee Chung-Yong, who both endured long-term injury absences.