Lloris was stretchered from the field screaming in pain after dropping a cross before falling backwards and landing badly as he conceded Brighton's opening goal at the Amex.
Pochettino lost for words as Brighton compound miserable week for Spurs
"Hugo Lloris has undergone further assessment this morning after sustaining a dislocated elbow in our match against Brighton on Saturday," Tottenham said in a statement on Monday.
"The findings have shown that although surgery will not be required, our club captain has suffered ligament damage and is not expected to return to training before the end of 2019.
"Hugo is currently in a brace and will now undergo a period of rest and rehabilitation under the supervision of our medical staff at Hotspur Way."
The news is another hammer blow to Tottenham's hopes of turning around a poor start to the season.
Mauricio Pochettino's men have won just three of their opening 11 games in all competitions and were thrashed 7-2 at home by Bayern Munich in the Champions League last week.
Spurs must stick together after Bayern thrashing: Pochettino
Argentine stopper Paulo Gazzaniga will now assume the role of Pochettino's first-choice goalkeeper for the forseeable future.
Lloris will also miss Euro 2020 qualifiers for France against Iceland, Turkey, Albania and Moldova.
"It is difficult to say exactly how long he will not be available," said France boss Didier Deschamps on Monday.
"What matters to us right now is that he will not be with us for this round of games or for the next."
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