Tsonga, runner-up to Andy Murray in 2011, suffered the injury at the French Open where he was forced to retire in the third round against Ernests Gulbis.
"I am very disappointed," Tsonga, 31, said in a statement.
"It is one of my favourite tournaments, home of some very happy moments for me on the court -- reaching the top 100 for the first time and playing in the final -- and I was looking forward to coming back."
Defending champion Andy Murray will be aiming for a record fifth title when the event gets underway on Monday.
(Reporting by Martyn Herman; Editing by Toby Davis)
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