The Reds forward picked up a suspected hamstring injury in the first half of Liverpool's 2-1 win over Wolves last week.
Speaking at his pre-West Ham press conference, Klopp confirmed Mane is set to miss Wednesday night's trip to the London Stadium.
The winger is unlikely to take part against Southampton at the weekend either, with a return date after the winter break more likely.
“Sadio will not be involved for West Ham and probably not for Southampton,” Klopp said.
“After that he should be then fine. The week we have then after that is for him perfect to get back on track.
“He has a small muscle tear, which is serious enough to keep him out. We were lucky with the injury as well, so it was not that serious.
“But of course, when you have three games in a week then that means he is out for these three games.”
Mane has enjoyed a hugely successful campaign so far and is an integral part of the way the Reds attack, especially linking with full-back Andy Robertson on the left-wing.
Liverpool should be able to cope against West Ham and Southampton without him, but the hope will be he can be at his best for Liverpool's Champions League tie against Atletico Madrid on February 18.
The Reds play Norwich away from home three days prior, so a return from injury against Daniel Farke's side could well be his target in order to get up to match fitness.