The Dutch attacker awkwardly jarred her knee towards the end of the first half and had to be carried off on a stretcher, much to the concern of her teammates and Jonas Eidevall.
Arsenal - who are already without Beth Mead for the long-term due to her ACL rupture - would concede the game's only goal just after Miedema was taken off, although there was an air of controversy about the winner.
A long pass from Selma Bacha into the box was met by Delphine Cascarino, who headed the ball across for Melvine Malard, but the ball surpassed her teammate and ended up in the back of the net off of Frida Maanum.
Replays showed that Malard was in an offside position as she challenged for the ball, but the goal was allowed to stand, and the Gunners' poor final pass let them down as they tried to claw their way back into the game.
It took until second-half injury time for Arsenal to carve out any more meaningful opportunities, as Lina Hurtig's goal-bound effort was blocked by Christiane Endler, who also did well to keep out Stina Blackstenius at her near post a few seconds later.
However, Arsenal's 5-1 win over the reigning champions earlier in the season meant that they only needed to avoid defeat by four goals or more to progress, and Eidevall's side are now guaranteed a top-two finish in Group C.
Arsenal will aim to seal top spot when they meet basement side FC Zurich next Tuesday, while Chelsea will also look to progress to the last eight in tomorrow's Group A clash with Vllaznia.