Odegaard, 26, was the first to go off, replaced by wonderkid Ethan Nwaneri in the 38th minute due to an apparent shoulder problem.
The 23-year-old limped off on the 53rd minute of Arsenal's convincing win over newly promoted Leeds, having scored their second goal.
Thankfully for the two players, their teammates were able to get the job done in their absence, taking the north London club to the top of the Premier League.
Speaking to the press after the game, Arteta kept his cards close to his chest, saying: "Martin looked like a shoulder. We'll have a scan tomorrow, so we'll see.
"Bukayo had to come off when he was sprinting with a defender, he felt a hamstring, a different one (than last season). We'll have to speak to the doctors.
"We lost Kai, who is a massive player, and now Bukayo and Martin, that's why the squad has to be big."