England international Gomez was substituted after 23 minutes of Wednesday's 3-1 victory at Turf Moor following a robust tackle from Burnley's Ben Mee.
"The club can confirm Joe Gomez sustained a fracture to the lower left leg," the club's website https://www.liverpoolfc.com said. "Gomez's injury was further assessed by the Reds' medical team at Melwood on Thursday.
"Initial indications suggest he is facing a spell of up to six weeks out of action, though this is dependent on how his treatment and rehabilitation programmes progress."
Liverpool manager Juergen Klopp was unhappy with the physical nature of some of Burnley's tackling and described some of it as like "10-pin bowling".
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(Reporting by Martyn Herman; Editing by Toby Davis)
