Sarr enjoyed a positive start to the encounter, driving home his second goal of the season to give Spurs the lead in the ninth minute.
Unfortunately for the 21-year-old, he was unable to make it to half time after being forced off just past the 30-minute park.
The midfielder underwent treatment by the club's medical staff on the pitch, before he made his way off to be replaced by Oliver Skipp.
The Senegal international was visibly upset as he left the field, with the injury issue appearing to place doubt over his involvement in the upcoming African Cup of Nations.
Speaking to reporters after the home victory, Tottenham boss Ange Postecoglou provided an update on Sarr's fitness status.
Postecoglou said: "Pape felt his hamstring and he's emotional because he wants to go away with his national team. It's a big tournament for them.
"It's kind of the way our season has gone. He was so good again early in the game, apart from his goal, and then he gets an injury.
"Disappointing for him but I am hoping it is not too serious and he can still go away and contribute to his country."
In addition to Sarr, substitute Alejo Veliz was unable to complete the match due to an injury that forced Tottenham to negotiate stoppage time with 10 men.
"Alejo was in a lot of pain," Postecoglou added. "We'd already done our substitutions so we were trying to get it out to him to just lay down so we can get him off.
"But it just shows the character of the boy because he knew we had no more substitutions and he just wanted to keep going."
Postecoglou will be hoping that the injuries to Veliz and Sarr are not too serious, with the Spurs boss already contending with a number of absentees.
Tottenham's injury list currently features Cristian Romero, Micky van de Ven, Ryan Sessegnon, James Maddison, Manor Solomon and Ivan Perisic.
In more positive news, Rodrigo Bentancur played nearly 60 minutes in Sunday's win after recovering from an ankle problem earlier than expected.