The 19-year-old missed the Tractor Boys' long-awaited first win of the season against Derby after suffering an injury to his hand during a practice match.
"Tommy hurt his hand in the last seconds of a practice match on Thursday," Keane told the club's official website.
"It was a nasty injury with two fingers dislocated and one of the bones coming through his hand so we had to take him straight to hospital.
"He had the operation on Thursday night and will be out for two or three weeks.
"It's a blow because he's been doing well for us. He's a tough lad though and hopefully he will be back after the international break is over."