Archer has already returned to action in the Indian Premier League after sitting out four matches. His coach at the Mumbai Indians, Mark Boucher, said on April 8 that he had picked up a "little niggle".
The Telegraph reported on Tuesday that Archer had travelled to Belgium for the procedure.
Archer has made two appearances for Mumbai this season, picking up two wickets. He was rested for Tuesday's defeat to Gujarat Titans but could return against Rajasthan Royals at the weekend.
Archer, who picked up 22 wickets for England in the 2019 Ashes, has not played a test since February 2021 due to elbow and back injuries. He made his comeback after 17 months out in late January.
Sussex head coach Paul Farbrace said last month Archer was unlikely to play any red-ball matches before the Ashes.
The opening Ashes test will be held at Edgbaston from June 16.
