Walcott out of England's trip to Poland
Walcott was clattered by San Marino goalkeeper Aldo Simoncini five minutes into England's 5-0 Group H victory at Wembley on Friday and spent the night in a London hospital under observation.
"He was monitored overnight as a precaution and following scan results today will return to his club [Arsenal] for further treatment," a statement said.
England coach Roy Hodgson was critical of Simoncini's clumsy challenge which flattened Walcott, suggesting the keeper should have been sent off for the tackle.
"I think if I describe it as a reckless challenge I am being very kind," Hodgson told reporters after the win had put England three points clear at the top of the group with seven points.
"It was a very fierce challenge. I don't believe for one minute there was any malice when he went for the ball but it was a very bad challenge."
Walcott's absence will be a blow to England as they prepare for what will be a much tougher assignment in Warsaw.