Hayes, who played the whole match, will be released from hospital on Tuesday and should be available to face Scotland at Lansdowne Road on March 11.
Ireland coach Eddie O'Sullivan said: "John got a viral infection and high temperature because of the demands and exertion of the game.
"He went to hospital for observation and his condition has stabilised. We expect him to be released in the next 24 hours.
"He will return home for the rest of the week and we expect him to report to the camp on Sunday. There is no risk to his participation against Scotland."
There was a positive update on Hayes' fellow front row Marcus Horan who was stretchered off in the 72nd minute following a collision with Gethin Jenkins.
Horan sustained damage to his neck but O'Sullivan eased concerns over his health immediately after the game and has now confirmed he will also be ready for Scotland.
"Marcus is quite stiff after the knock he took but he's fine and we expect him to be back in full training next week," he said.
Lions lock Paul O'Connell missed the Wales match with a shoulder injury but his rehabilitation will be completed in time for the crunch showdown with Frank Hadden's men.
"Paul is coming on all the time. He was close to being able to play but the risk was that if he sustained a knock on it the rest of his tournament would be jeopardy," O'Sullivan said.
"On balance it was sensible to rest him and we have every confidence he will be good to go for Scotland."