The 28-year-old suffered the problem in the warm-up before Saturday's 2-1 home defeat to Queens Park Rangers. His late withdrawal meant Dominic Iorfa was drafted in at centre-back, with David Bates taking Iorfa's place on the bench.
Lees, who has clocked up over 200 appearances since joining the Hillsborough club in July 2014, has continued his rehabilitation from injury with Doctor José Manuel Sánchez at the CEREDE Sports Rehab Centre in Barcelona, Spain.
Sanchez, a world-renowned expert, has previously worked with Sam Hutchinson and Gary Hooper, who was released by the Owls last summer. He has also helped Sevilla's Daniel Carrico and former Arsenal star Mike Arteta in the past.
On Lees' absence against QPR, Wednesday caretaker boss Lee Bullen told The Star: “His hamstring tightened up. There was no point taking a chance on that.
"We didn't want to lose him but if you put Tom in and it tears then you’re losing him for six weeks.
“For the sake of one game I think it was the right decision."
The Owls are hopeful Lees will be available for selection when they travel to managerless Huddersfield Town after the two-week international break.