The injury to Frimpong leaves Slot short on options at right-back.
Frimpong was signed from Bayer Leverkusen for £29.5m in May to replace Trent Alexander-Arnold, who left to join Real Madrid.
Northern Ireland defender Conor Bradley only returned to first-team training on Thursday, while Slot said Joe Gomez, who has suffered long injury lay-offs during his career, was unable to train for three days in a row after replacing striker Hugo Ekitike late on against the Cherries.
“Jeremie [Frimpong] has a very positive injury record. Conor [Bradley] was out once or twice last season. These things happen,” said Slot.
“At the moment, we only have two injuries, but unfortunately it is two in the same position. The good thing is we have other players that can play there. Wataru Endo played there, Dominik Szoboszlai also.
“Joe Gomez is definitely one of them, but for him to already play 20 minutes – that is already quite a lot.
“He is training with the team, so let’s see where he is and if he can be involved on Monday. You cannot prepare for two injuries in one position.”
