"It's a pity I missed yesterday's match with my back injury," Ozil wrote on his Instagram account after sitting out Arsenal's 5-0 rout of Burnley on Sunday.
"It'll need some time, but I'm sure I'll fully recover in time for the World Cup."
With just over five weeks until the World Cup starts on June 14, the Arsenal playmaker joins Manuel Neuer and Jerome Boateng, who also face a race against time, on the casualty list.
Arsenal manager Arsene Wenger had revealed before kick-off that Ozil was expected to miss the rest of the season with a back ailment.
Germany's first World Cup group match is against Mexico in Moscow on June 17. They also face Sweden and South Korea in Group F.
Neuer, Germany's captain and goalkeeper, has not played since fracturing his foot last September.
Burly centre-back Boateng injured his groin in Bayern Munich's Champions League semi-final defeat at home to Real Madrid a fortnight ago.
Germany coach Joachim Loew will announce his World Cup squad on May 15.
Ozil, Boateng and Neuer are all expected to be named, but will have to prove their fitness during a two-week training camp in northern Italy.
"Right now, we all keep our fingers crossed that Jerome's injury somehow will still heal well and also that everything continues as planned with 'Manu'," said Germany's team director Oliver Bierhoff last week referring to Neuer.
Fringe players Lars Stindl, who scored the winning goal for Germany in the 2017 Confederations Cup final, and ex-Arsenal winger Serge Gnabry have both already been ruled out of the World Cup by injury.