The news is a hammer blow for the 23-year-old, who had been finding his feet this season after injury troubles last term.
Smith Rowe started Arsenal’s 5-0 win over Sheffield United on Saturday, his first in the Premier League for 524 days.
He had been expected to start again in Wednesday’s Carabao Cup fourth round tie away at West Ham, which Arsenal lost 3-1, but was left out of the squad.
Arteta confirmed after the game that Smith Rowe has a knee injury and will be out of action for a few weeks.
“He’s got an injury in his knee and he’s going to be out for weeks,” said Arteta.
Arsenal are already struggling with a few injuries, as they have at several points so far this season.
Thomas Partey is currently sidelined with a thigh injury and is expected to be out of action until December.
Striker Gabriel Jesus is also on the sidelines at the moment after injuring his hamstring against Sevilla last week.
The Brazilian is expected to be out of action until at least the international break later this month.