Lacazette, who came on for Arsenal as a 65th-minute substitute during their 1-0 defeat to Tottenham at Wembley on Saturday, is expected to return in March after a successful operation on his left knee.
Arsene Wenger will be without the £52m striker for the Carabao Cup final against Manchester City on February 25, live on Sky Sports, as the two sides vie for the first major piece of silverware of the season.
Lacazette will also be absent for the league meeting against Manchester City at the Emirates, which takes place a week after the two sides meet in the Carabao Cup final at Wembley.
Arsenal travel to Sweden to face Osterunds FK in the round of 32 in the Europa League on Thursday, and alongside the missing Lacazette, Aaron Ramsey is also a doubt for the midweek game as he recovers from a groin strain.
Lacazette, who arrived from French club Lyon in the summer of 2017, was criticised by Arsenal fans for his display against their north London rivals on Saturday, after he spurned an opportunity to level the game in stoppage-time.
The 26-year-old has struggled for form since the turn of the New Year with his only goal in 2018 coming in Arsenal’s 4-1 win over Crystal Palace in January.
The north London derby disappointment was Arsenal’s third defeat in five Premier League games and they are now eight points adrift of fourth-placed Chelsea.