The 22-year-old featured off the bench in the 3-1 defeat at Old Trafford on Sunday, but picked up a minor injury during the warm-down.
There was hope that the problem wouldn't be too serious and that Smith Rowe would be fit to start his first match of the season on Thursday.
The England international missed the Premier League opener with a groin injury, and has been on The bench, playing second fiddle to Gabriel Farinelli since.
But in a blow for the Gunners and Smith Rowe, he hasn't travelled with the squad to Switzerland, having been left in England to recuperate.
Boss Mikael Arteta has even stated that the former RB Leipzig loaner hasn't trained this week.
And he has revealed that Smith Rowe has been suffering discomfort in recent weeks.
The news will ask questions as to why the Spaniard decided to throw the youngster off the bench in four out of the last five games if he has been experiencing pain.
Speaking in his pre-match press conference, Arteta said: "He felt discomfort in an area that [he’s been dealing with] now for a few weeks.
"He wasn’t comfortable after the game, and he hasn’t trained in the last few days, so he’s out of the squad.