Defeat to the Bundesliga outfit follows on from a 3-1 loss against Real Betis in Dublin after opening their summer schedule with back-to-back wins over MK Dons and Girona.
Next up for the Gunners is a final friendly against Cesc Fabregas' Como on August 12th followed by the FA Community Shield showdown with Manchester City four days later.
Following the Dortmund defeat, Arteta confirmed all remaining players away on post 2026 FIFA World Cup breaks are due back in training in the coming days, but William Saliba and Jurrien Timber are both out of the picture for some time.
Saliba suffered a back injury at the World Cup, and is not due back in action until at least October, with Timber forced to fly home from Arsenal's training camp in Spain due to a groin issue.
The issue was initially flagged up as a precaution, but the Dutchman has not featured since, and Arteta remains uncertain on his comeback date.
"Jurrien is progressing well, but it will be weeks before he's back. William Saliba is in rest mode.
"We know we have lost incredible players in both of them."
Arsenal start their title defence at home to Coventry City on August 21st with Ben White set to start the campaign at right-back.