The Ulster player was injured late in the 22-9 defeat and Leinster's Fergus McFadden takes his place in the squad.
Conor Murray and Johnny Sexton are expected to be fit for the Dublin game after picking up injuries in Cardiff.
Scrum-half Murray sustained a shoulder injury while fly-half Sexton was not concussed after a head knock.
Sexton was taken off for a head injury assessment and returned after clearing the medical tests.
"He has a big black eye - with any contact to the head there will be an HIA done," said Ireland team manager Paul Dean on Monday.
"There are three stages to that. He came through all three of them no problem and there's no concern for concussion."
Murray suffered a shoulder injury while attempting to tackle Welsh try-scorer George North in the first half.
Dean added: "Conor's fine - he got a stinger. The full power [of the arm] is slow to come back. It didn't come back quickly enough for him to stay on the pitch but it's come back 100% now."
Bowe was introduced in the 79th minute and sustained the injury to his left leg just seconds later.
"It's a suspected fracture. We wish Tommy all the best and a speedy recovery," said Dean.
"It was very unfortunate. I don't think he was even on for a minute. We're really sorry for him."
Ireland's hopes of a third Six Nations title in four years were ended at the Principality Stadium.
Joe Schmidt's team stayed in second spot but eight points behind England, who are aiming for back-to-back Grand Slams.
Ireland wing Tommy Bowe will miss Saturday's Six Nations match with Grand Slam-chasing England after suffering a suspected broken leg against Wales.