The France international was carried off on a stretcher early in the 4-3 win against Leicester City and missed his country's friendlies against Brazil and Denmark.
"Hugo Lloris is still recovering after his problem against Leicester -- he is out," Tottenham manager Mauricio Pochettino said at a news conference on Thursday.
Michel Vorm will deputize for Lloris.
Spanish striker Roberto Soldado is also a doubt for the match at Turf Moor, where Tottenham need a victory to stay on the edge of the fight for a top-four finish.
Tottenham are in seventh place in the table with eight games remaining, six points behind fourth-placed Manchester United and with a far worse goal difference.
However, Pochettino said he hopes the quartet of players who featured for England on Tuesday against Italy will be have received a timely confidence boost.
Harry Kane started his first senior England international in Turin, while Andros Townsend came off the bench to score a superb equaliser. Ryan Mason earned his first senior cap while Kyle Walker was also involved.
"It's been a very good week for Tottenham," he said.
"The English players and others with their international teams have put in good performances. They are all fit and at a very good level."
(Reporting by Martyn Herman; editing by Toby Davis)
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