The Czech has been sidelined since June after suffering a knee problem while on international duty and was expected to return to full training later this month.
But Rosicky, 34, now looks set to miss at least another four weeks after undergoing a procedure on his knee.
"Tomas last Tuesday passed arthroscopic knee surgery. The recovery period is estimated at four to eight weeks," Rosicky’s agent Pavel Paska told iDNES.cz.
The Czech FA confirmed he will miss the country’s Euro 2016 qualifiers in September and say he faces a race against time ahead of games against Turkey and the Netherlands in October.
"He's had some treatment, though not anything big. But time is against us," added Miroslav Pelt, chairman of the Football Association of the Czech Republic.
Arsenal triggered a clause in Rosicky’s contract last season to extend his deal until 2016 and has revealed his frustration over a lack of playing opportunities last season.
