Marler fractured his leg in the warm-up of Harlequins’ win over Sale on Saturday.
“Harlequins can confirm today that Joe Marler has suffered a fracture to his lower left leg,” the club said in a statement.
“He will undergo a period of rehabilitation and is expected to be fit to play again in four to five weeks.”
England head coach Eddie Jones, who is scheduled to name his England squad on Jan. 20, faces a growing list of injury concerns as he mulls squad for the Six Nations opener against France on Feb. 4 at Twickenham.
With Marler and Mako Vunipola, who sustained a knee injury, on the sidelines, Jones is likely to hand a first test start to Leicester’s rookie prop Ellis Genge.