Arteta said 15-year-old Dowman suffered an ankle injury during a behind-closed doors friendly on Saturday.
The teenager has been withdrawn from Arsenal's Champions League squad, meaning he cannot play in the competition again until the knockout stages.
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Leandro Trossard has not travelled to Belgium for Arsenal's league phase match against Club Brugge after he sustained an injury in Arsenal's Premier League defeat at Aston Villa last weekend.
Declan Rice is also out through illness. Defensive trio William Saliba, Gabriel and Cristhian Mosquera and forward Kai Havertz remain sidelined.
Arsenal have suffered an extraordinary 95 injuries since the start of the last Premier League season -- second only to Brighton -- and 28 already so far this term, which is among the highest in the league.
But when asked if he is overtraining his players, Arteta said: "No, because we don't have time to train.
"Today we've done 20 minutes, so surely it's not because we over-trained the players.
"But obviously when you are missing players, you are loading other players and there is a consequence to that, and it's a really dangerous circle.
"You have to separate the kind of injuries. Some of them have been long-term, and some have been acute injuries.
"It's something that we are constantly looking at. We have played a lot of games with a lot of players missing and that puts a lot of stress, and then you get more injuries."
Reflecting on his latest setback with Dowman, Arteta continued: "It is part of the journey. I mean at some point when you play at this level, when you play in the position that he plays, when you play the manner that he plays, it was going to happen, and it has happened.
"It's not ideal. He picked up weeks, it could have been worse, and we learn from that and now use this time to continue to improve in his education, in everything that is related to professional football, his habits, the way he needs to develop his physicality as well and the understanding of the game."
In a rare injury boost to Arteta, Gabriel Jesus could make his first Arsenal appearance in 332 days against Club Brugge.
Jesus has been sidelined since he ruptured the anterior cruciate ligament in his left knee in Arsenal's FA Cup third-round defeat against Manchester United on Jan. 12.
Arsenal have confirmed the 28-year-old has now been registered for their Champions League squad. He takes the place of Dowman.
Jesus was an unused substitute in Arsenal's 1-1 draw Chelsea last month and the following 2-0 home win over Brentford.
Mikel Merino has recently led the line for Arsenal, with all of Viktor Gyökeres' last three appearances coming as a substitute following a groin injury.
The Gunners are bidding to bounce back from their 2-1 Premier League defeat at Aston Villa on Saturday by making it six consecutive wins in the Champions League.
