The 26-year-old had an arthroscopy in London on Tuesday morning and the procedure was described as a “success” by the Gunners.
A statement on the club’s website read: “The minor procedure was a success and he will now undergo a period of rehabilitation.
“It is envisaged that he will return to the squad within four to six weeks.”
The France international has often cut a frustrated figure since his £52million move from Lyon in the summer.
Lacazette has scored nine goals in 29 appearances for the Gunners this term, but has just one from his last 13 outings in all competitions.
Pierre-Emerick Aubameyang’s arrival from Borussia Dortmund last month has raised further doubts over Lacazette’s role under boss Arsene Wenger.
Aubameyang is ineligible to play in the Europa League, though, leaving Arsenal short of options in attack for the first leg of the knockout tie with Ostersunds in Sweden on Thursday.
Lacazette will also miss the second leg a week later, as well as the Carabao Cup final against Manchester City on February 25 and key Premier League fixtures.