Gomez was substituted after just 23 minutes at Turf Moor following a firm challenge from defender Ben Mee that riled Liverpool manager Jurgen Klopp.
The 21-year-old was assessed by the club's medical staff after the match, and is now set to be sidelined until the New Year.
A club statement read: "Liverpool can confirm Joe Gomez sustained a fracture to the lower left leg during the 3-1 win at Burnley on Wednesday night.
"The defender needed to be substituted after 23 minutes at Turf Moor following a challenge from which he was unable to continue. Gomez’s injury was further assessed by the Reds’ medical team at Melwood on Thursday.
"Initial indications suggest the 21-year-old 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 came from a goal down to beat Burnley and remain just two points behind Manchester City at the top of the Premier League, but Klopp was left dismayed by the force of some of the home side's challenges during the game.
"We won the game but the challenges from the beginning, the sliding tackling on that wet ground, I really think the referee should have said something earlier," he insisted.
"The injury threat is massive. That was hard. You get the ball, nice, but it's like bowling because you get the player as well. It happened four or five times.
"The first three or four challenges everybody likes it. I know that. It's part of football but it lead to the situation. OK, no foul but Joe Gomez is injured."
Burnley boss Sean Dyche spoke out in support of Mee and added: "I was a bit confused [by the reaction]. There were some excellent tackles. The only one that was questionable was Bardo's [Phil Bardsley on Alberto Moreno].
"Ben Mee's was a fantastic tackle and I think Gomez realised that. We send him our best if there is any injury but it wasn't from a bad tackle. Of course football managers can question whatever they like but I don't think they can reinvent the rules.
"I don't think there's many fans in this country that want to see tackling go out of the game."
Gomez has established himself as a key figure for Liverpool this season, starting 12 of their 12 Premier League matches and forging a formidable partnership with Virgil van Dijk in the heart of defence.
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