The 29-year-old sustained the damage late on in the 3-1 win over Hull City on Tuesday night, shortly after netting the second of his two goals.
Gestede underwent a scan on the injury and it has been confirmed that his 2017-18 campaign is over, which Pulis admits is a 'real disappointment' for both the Benin international and Boro.
"He won't play again this season, we don't think," he said at his weekly press conference. "It's a massive blow for us as a football club. Out of all of the strikers, he's looked the most likely to score in the games we've played.
"We're really disappointed, but we've got options up there, whether it's Patrick [Bamford] or Britt [Assombalonga], they have to step up to the plate."
Former Cardiff City and Aston Villa ace Gestede had found the net four times in 21 appearances for Middlesbrough this term prior to picking up the injury.