The 22-year-old, who joined the club in the summer transfer window, was forced off during the first half of Villa's win over Southampton before the international break.
Further tests confirmed Boubacar, signed from Marseille, had sustained ligament damage which will require a lengthy spell of rehabilitation.
"Kamara will be missing until after the World Cup with a knee ligament injury, suffered during the win over Southampton," a Villa statement said.
Kamara, who has won three caps for France, had been called up for the latest round of Nations League matches before his injury.
The loss of Kamara is another setback for Villa, whose Brazilian defender Diego Carlos ruptured his Achilles in only his second appearance for the club.
Left-back Lucas Digne was also forced to pull out of the French squad because of a heel problem, which Villa said would make him "unavailable in the coming weeks".
"It is not ideal, we have had better days on the injury front," Villa manager Steven Gerrard said at his pre-match press conference on Friday.
"Boubacar will be missing until after the World Cup unfortunately, so that is a huge blow.
"It is him and obviously Diego Carlos, two of our signature signings, who are going to be missing for a large part of the season."
Villa head to Leeds on Sunday out to extend their unbeaten run to three games, having drawn against Manchester City and beaten Southampton earlier this month.
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