However, Hodgson says that Caulker will recover in time to travel with the squad for the match in Kiev.
"Steven unfortunately turned his ankle in training," Hodgson said in a press conference. "It's not a very serious matter but it will keep him out of the game [against Moldova]. It won't keep him out of the Ukraine game.
"He's expecting to do some running [on Friday] evening after the game with the players who don't play but he won't be on the bench."
England host Moldova at Wembley on Friday night with kickoff at 8pm.