Media reports said the Uruguayan may be out for three months.
Spurs are also without attacking midfielder James Maddison due to an ACL injury, and fellow midfielder Lucas Bergvall also picked up an injury during the Bournemouth game and missed the weekend's 2-1 FA Cup loss to Aston Villa.
"We can confirm that Rodrigo Bentancur has undergone surgery on his right hamstring... and will now commence his rehabilitation with our medical staff," Spurs posted on X on Tuesday.
Media reports also said that Spurs are in talks to sign England midfielder Conor Gallagher from Atletico Madrid to boost their bid for a top-eight finish in the Champions League in order to qualify directly for the last 16.
Spurs, who play Borussia Dortmund and Eintracht Frankfurt this month, are a point below eighth-placed Atletico in the European competition.
The London club are 14th in the Premier League standings and host West Ham United on Saturday.