The 27-year-old midfielder completed a move to Stamford Bridge from Leicester City on transfer deadline day last month as Conte moved to bolster his squad before the window closed.
The former Leicester star has not made an appearance this season and it looks as though he will be forced to wait a number of weeks before making his Chelsea debut.
Conte confirmed the injury blow at his pre-match news conference at Chelsea’s Cobham training ground on Friday and admitted his disappointment that Drinkwater will not be available for selection for a number of weeks.
Conte told his pre-match news conference: “I think it’s very difficult to see him before the international break. He needs time to recover. It’s a pity because he was starting to work and to improve his physical condition.
“Now we have to move all these situations. And in two, three weeks, four weeks, I don’t know.”
The Chelsea manager is currently preparing his side for their crunch Premier League clash against Arsenal at Stamford Bridge on Sunday afternoon.
The Blues have been in good form in recent weeks, winning their last three games in the top flight, before also thrashing Qarabag in their Champions League opener on Tuesday night.
Arsenal, meanwhile, head into the game after victories at home against Bournemouth and Cologne.
The Gunners are looking for their first Premier League points on the road this season.
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