Frida Maanum will miss Arsenal's game against Bristol City, but could return the following week to face Leicester at Emirates Stadium.
The midfielder collapsed during the Conti Cup final win over Chelsea, and Arsenal said tests on Maanum showed "no obvious cardiac causes."
Head coach Jonas Eidevall said: "everything is looking good and that's the most important thing. She's on a graduated, monitored protocol now to return to play.
"She will not be available for selection on Sunday but after that, if everything goes as planned, it looks promising for her to be available to play again."
"We're not going to disclose any medical findings and so on here publicly. But what I can assure you is that the support around Frida has been phenomenal and the monitoring and the protocols and the testing have been of the highest of standards to ensure both her mental health and wellbeing, but also to ensure a really safe protocol in return to play."
Regarding any other injury news for Eidevall's squad, the head coach said: "They're just coming back in here today, so it's screening and we need to see them on the pitch. So the one we have an update on is Frida and that the game will come too early for her, but for the rest, we'll wait and see."