Lacazette has hit two Premier League goals this term but will sit out Monday's (AEST) trip to Watford.
He will also be sidelined when Arsenal gets its UEFA Europa League campaign up and running away to Eintracht Frankfurt next week.
Arsenal indicated Lacazette has been playing through pain in his left ankle but is "likely" to return next month.
"After assessments to an ongoing ankle issue, we have advised that Alex will need to rest and strengthen his ankle to regain full fitness," a club medical statement read.
"Alex has been playing through this injury for several weeks."
Matches set to be missed by Lacazette include a trip to Manchester United in the Premier League on 1 October.