Wanyama, who is the only player to have featured in all 28 of his club's Premier League fixtures this season, picked up the problem in Saturday's victory at Burnley.
The Kenya international was involved in an aerial collision with Ashley Barnes and initially appeared to shake off the problem before eventually being withdrawn on the stroke of half time.
Wanyama may yet be able to take his place in the starting line-up against Paul Clement's side but Pochettino opted to remain coy on the midfielder's chances of recovery before the scale of the injury has been evaluated.
Pochettino said: "We need to assess him on Tuesday.
"Today he wasn't on the pitch. We'll see. He will have a chance to be in the squad but we need to assess him tomorrow."
Wanyama has established himself as a key presence in Pochettino's midfield since joining Spurs from Southampton last summer.
The 25-year-old's form has restricted Eric Dier's game time in midfield but the England international could be deployed in the centre of the park if Wanyama fails to recover.
Dier was ushered into a midfield role alongside Mousa Dembele at Turf Moor and scored his first goal of the season as Pochettino's side cut Chelsea's lead at the top of the table to seven points.
Spurs have proven they can operate in a 3-5-2 and 4-2-3-1 formation and Pochettino has plenty of opens open to him ahead of tomorrow's visit to Liberty Stadium.
Meanwhile, Pochettino has confirmed Harry Winks is unlikely to play again this season after sustaining a serious ankle injury at the weekend.