Arsenal hope that Lacazette will help them return to the top four of the Premier League table and qualify for the UEFA Champions League - something they missed out on last season for the first time since Arsene Wenger took over as manager in 1996.
"He had a little abdominal strain that he caught on Sunday morning in training and he had a scan two days ago", Wenger told a news conference.
"I don't know if it is two weeks or one more week, but he will not be available".
Arsenal turned around the league's first Friday opener in the closing minutes at Emirates Stadium.
When asked if Arsenal have received any bids from PSG for the 28-year-old, Wenger replied: "I can not tell you that".
"We are still open", he said. "I have had no contact with PSG". Alex Oxlade-Chamberlain has also been linked with an exit along with Newcastle eyeing Lucas Perez.
Predicted XI: Cech; Holding, Mustafi, Monreal; Bellerin, Xhaka, Elneny, Kolasinac; Welbeck, Iwobi, Lacazette. I love this boy and think he is going to have a huge campaign - unlike Stoke...
"Last year he was much more stable".More news: Engineer behind controversial manifesto is out at Google
More news: Bayern Munich beats Borussia Dortmund to win 2017 Supercup
More news: Taylor Swift Expected to Testify in Groping Case Against Former Radio DJ
"I thought he was really unselfish for a player making his debut".
"He's very conscious of his qualities, he was not always".
He has said he intends "to focus completely on the Premier League", but if such an approach fails to yield a title challenge, he can expect the protests to ramp up quickly.
'There's no relation between clubs and countries and seasons and periods, so obviously there is no guarantee.
His brittle defence has not eased any worries going into the game and safe to say, they are not happy with that performance in the slightest. We got a central midfielder, a striker, obviously the 25 per cent would be for a player from the sides, but we have players. We want him to be a nuisance. "That's what we want to achieve this season".
However, the United boss insists it is not just down to the Belgian to pick up the slack this term, telling a news conference on Friday: "What I had in other clubs was more players scoring goals".
Wenger has also been impressed by another new signing, defender Sead Kolasinac, who even scored his first Arsenal goal with the equaliser against Chelsea in the Gunners' eventual Community Shield win.