The club are sixth in the WSL table after winning just one of their opening four league matches and suffered a 5-2 loss against Bayern Munich in the Champions League last week.
Arsenal sporting director Edu said on the club website: "We thank Jonas for his commitment to the club and achievements here since joining us in 2021.
"We have great respect for the dedication and commitment he showed to our women's first team and recognise the role he has played in the growth and development of Arsenal Women."
Frustration from the Bayern loss was compounded by a 2-1 home defeat against Chelsea in the WSL at the weekend.
Asked about the pressure on his own position afterwards, Eidevall said: "I gave absolutely everything today in the preparation for this game, I think you can see that the players gave absolutely everything on the pitch.
"I think that's the part you can control as a coach. And, just like focusing on the next match, I need to focus on the things I can control."
The Swede, 41, joined the Gunners from FC Rosengard in June 2021 and led them to two League Cup titles and the semi-finals of the Champions League in 2023.
Arsenal have not won the WSL title since 2019, with Chelsea dominating in recent seasons.
Assistant coach Renee Slegers will take charge of the team on an interim basis.
