The midfielder, one of Tottenham's outstanding players this season, suffered a groin injury in the return leg of the quarter-final tie at Manchester City and Spurs manager Mauricio Pochettino believes he will not be fit for another two weeks.
That would rule Sissoko out of the north London club's home leg against Dutch giants Ajax on April 30, with Tottenham already missing South Korea star Son Heung-min through suspension.
Son has been a key man for Spurs while England captain Harry Kane has been sidelined with an ankle injury.
"Moussa Sissoko is not going to be fit, maybe for the next two weeks, we hope he can recover before but I am not so optimistic," Pochettino said ahead of Tuesday's Premier League match at home to Brighton.
"Harry Winks we don't know because it is a problem that is one day very good, next day not very good, it is about assessing each day.
"We hope he will be available for Tuesday but we are not sure."
There are also doubts over the fitness of France goalkeeper Hugo Lloris, with Pochettino saying: "Lloris I hope yes, we are going to assess, we have a training session and we hope it is not a big issue, we hope he is going to be available."
'Thinking in the today'
Tottenham may have lost to Manchester City in their second game at the Etihad inside 72 hours but they remain firmly in the hunt for a top-four finish in the Premier League after both Arsenal and Manchester United lost as well at the weekend.
If Spurs beat Brighton and West Ham in back-to-back games at their new ground they will be on course for a top-four finish that would qualify them for next season's Champions League regardless of whether they win this season's edition of European club football's elite competition.
"We are not thinking of Ajax," Pochettino said. "We showed at Manchester City that we are thinking in the today and that competition, the Premier League."
The Argentinian added: "Now our energy is in Brighton. It is so clear that we have two objectives -- one is to be in the top four at the end of the season and the other is to beat Ajax, but we need to go step-by-step.
"The players, they know it, I think the behaviour and the mentality is perfect."
Despite concerns a mid-season move to a new ground may prove unsettling, Pochettino's men have won all their three matches so far at the Tottenham Hotspur Stadium, scoring seven goals and not conceding any in the process.
"We hope we can keep going, getting the same result," said Pochettino.
"It is going to be fantastic and it is going to be helpful for us playing in the new stadium with our fans and we hope and wish to repeat the performances of the previous results."