Assou-Ekotto, 25, has withdrawn from Cameroon's African Nations Cup squad and requires an injection next week for the injury, but it is understood he will not require an operation.
It is a double blow for Spurs manager Redknapp as England winger Aaron Lennon has been ruled out for a fortnight with a similar problem.
"Benoit is having an injection on Monday," Redknapp said. "And he will be out for a few weeks.
"He has been terrific. Two terrific players, him and Lennon, have both picked up groin strains. It's a big blow to us. They are two outstanding players."