"Henderson has successfully had a corrective procedure carried out on the adductor injury. He will begin a rehabilitation programme immediately," Liverpool said in a statement.
The statement added: "No specific timescale is being placed upon his return; however, he is ruled out initially until after the March international break."
Speaking in a news conference ahead of the trip to Sheffield United on Sunday, Liverpool boss Jurgen Klopp said he is confident that Henderson can return to action before the season ends.
"With so many injured players who are not available at the moment, and with most of them leaders, they are here doing their rehab and they all have to be influential," he said.
"When Hendo is back he has to play this role while doing his rehab. It is not a quick one but we all hope there is a possibility for him to play a few games this season."
Liverpool are sixth in the table with 40 points from 25 games, five points adrift of fourth-placed West Ham United.