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.
"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.
Argentine stopper Paulo Gazzaniga will now assume the role of Pochettino's first-choice goalkeeper for the forseeable future.