The 26-year-old had an arthroscopy in London and the procedure was described as a "success" by the Gunners.
"The minor procedure was a success and he will now undergo a period of rehabilitation," said a statement on the club's website.
"It is envisaged that he will return to the squad within four to six weeks."
Arsenal signed Lacazette from Lyon for a then club-record £46.5 million (52 million euros, $65 million) in July last year and he had a bright start to his career in London but has only scored once in 13 matches since December.
He is the club's top scorer this season with nine goals and netted twice for France in their friendly against Germany in November.
The timing of his injury could not be worse for the forward, with Pierre-Emerick Aubameyang arriving at the club last month for a new record fee of £56 million.
But Aubameyang is ineligible to play in the Europa League, leaving Arsenal short of options in attack for the first leg of the knockout tie against Ostersunds in Sweden on Thursday.
Lacazette will also miss the second leg a week later, as well as the League Cup final against Manchester City on February 25.