Hodgson revealed Walcott would spend the night in hospital after being taken off following a 10th-minute challenge by San Marino goalkeeper Aldo Simoncini.
Hodgson told ITV1: "It was a very bad challenge and he's in hospital and will stay in hospital overnight.
"He's having scans and tests and we can only hope it isn't too bad, but it was a very poor challenge and we should have been up after three minutes with a penalty.
"It's never easy when 10 players are parked in the penalty area but I was very pleased with the way we kept playing football from the first minute to the very last.
"Five goals is a good result and there was a good result also for us in Moldova, so it's been a very satisfying week's work."