Walcott suffers hamstring strain
Walcott, 23, inspired a comeback win over Sweden as a substitute on Friday, scoring England's second goal and setting up Danny Welbeck for the third to seal a 3-2 victory.
"Unfortunately, he had a slight setback in training today so that's the major concern for him," Hodgson said.
"He felt the hamstring that, of course, kept him out for so long at the end of last season and we were slightly concerned when he came to us.
"It was a precaution to take him from the field because he felt a slight tightness there so really whether he is a real contender for a starting position will depend on what the medical people can tell me."
England need a draw against Ukraine to reach the quarter-finals and will be boosted by the return of striker Wayne Rooney from a two-match suspension.