Goalkeeper Lloris sustained the injury during Saturday’s 1-1 draw with Everton.
It means he faces a race against time to be fit for Spurs’ European opener, which will be played on September 13 or 14.
The Frenchman is likely to sit out Tottenham’s next three Premier League matches, including home games against Crystal Palace and Liverpool, as well as a trip to Stoke.
A club statement, released on the official club website, read: “Following further assessment and scans of the left hamstring injury sustained by Hugo Lloris in the 1-1 draw at Everton on Saturday, we can confirm he is expected to be out of action for around four weeks.
“Our captain left the field during the first half at Goodison Park and our medical team will continue to monitor his progress during his rehabilitation to determine when he will be ready to return to training.”