The Ivory Coast hitman is only just starting his basic pre-season training regime after a knee operation and will miss the home visit of Portsmouth and the away match against Wigan Athletic.
Chelsea boss Luiz Felipe Scolari said: "Didier will not play in our first game and will probably miss the second against Wigan.
""If there are no more problems he should be ready for the game after that, Tottenham on 31 August."
Chelsea hammered AC Milan 5-0 yesterday with Nicolas Anelka hitting four.
He is expected to start against Portsmouth on August 17 but with Salomon Kalou at the Olympics and Andriy Shevchenko behind in his pre-season schedule, Chelsea could find themselves using midfielder Joe Cole as a second striker.
THis would of course alieviate the congestion for midfield places where everyone appears to be in top form.
Michael Ballack will most likely give way as he joined the squad late following the Euro 2008 championships.
With Drogba and Frank Lampard expected to put pen to paper within the next two weeks on new deals, Chelsea can be confident that their squad will be stable for the next few seasons.
Robhino is still a Chelsea target and would be the only addition to the squad.
If they nab the Brazilain wideman, then they are expected to make Shaun Wright-Phillips available for transfer.
However SWP is happy at Stamford Bridge and reluctant to move.