The 25-year-old underwent surgery on Sunday at the Queen Elizabeth Hospital in Gateshead after injuring his thumb in last week's 31-31 draw with the British Army in Portugal.
The utility back, who crossed the whitewash twice in the entertaining draw, will miss next week's Aviva Premiership trip to Gloucester followed by Saracens at home on 20 April and London Wasps at Adams Park on the final day.
"It was a very frustrating day yesterday to be told that I would be missing the rest of the season and it has certainly come at the wrong time," said Manning.
"I am not sure how I actually picked up the injury but after I scored my two tries I made a couple of tackles so it must have happened in the tackles," added the Kiwi.
Gary Gold's men beat the April snow and jetted off to sunny Portugal last week for some warm weather training ahead of the return of Premiership rugby.
Based at Browns Sports and Leisure Club in Villamoura, the Falcons were put through their paces in Portugal's southernmost city.
A try from England Sevens international Isosa Damadamu secured a hard-fought draw for the Army with Manning summing up the game.
"The match was a really good test for us and it was just unfortunate that we conceded the try at the end," he said.
"Portugal was really good and we tried to put things right for the Gloucester game - it could have been a lot sunnier though!"
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