Olympique Marseille's Remy was ruled out of action for up to four weeks with a thigh injury while Tottenham Hotspur's Kaboul suffered a re-occurrence of a knee injury.
Remy picked up a knock in Olympique Marseille's 3-0 victory over AJ Auxerre in Ligue 1 on Sunday, two days before France coach Laurent Blanc names his preliminary Euro 2012 squad of home-based players.
"He should be out for three or four weeks," Marseille said on their website.
"We'll see with the doctors but we need to know if we can have him on time for the start of the competition," Blanc, who will name a "larger than expected" squad on Tuesday because of the injuries, told Infosport+.
Blanc was more worried by Kaboul's injury, which flared up during Tottenham's final Premier League game against Fulham on Sunday.
"His case is the most worrying. It's an old injury he's had for two or three years. He will undergo checks today or tomorrow," said Blanc.
Kaboul was included in Blanc's 12-man preliminary squad of players based abroad.
Chelsea winger Florent Malouda also picked up a thigh problem at the weekend but Blanc said he had been replaced "as a precaution".
France are in Group B with England, co-hosts Ukraine and Sweden in the June 8-July 1 tournament.
They kick off their campaign against England in Donetsk, Ukraine, on June 11.
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