Eva is also considering her legal options after she had her role reduced following a spat with manager Jose Mourinho in the opening game with Swansea, according to reports.
Mourinho was upset with Carneiro, 42, and head physiotherapist Jon Fearn for entering the field of play during the 2-2 draw to treat Eden Hazard.
The Portuguese was visibly furious with their actions, and ran from his technical area to berate them. He later followed that by criticising Carneiro and Fearne in three separate media interviews, accusing them of not understanding the game.
The Football Association has confirmed it is looking into a complaint that the Chelsea manager used abusive language toward Carneiro, who has not been seen on the Blues’ bench since the incident.
Chelsea do not comment on internal staffing matters, but Carneiro has not reported for duty since her reprimand, while Fearn has continued to work.
Carneiro, who was due to return to work last Friday, could have grounds to launch claims of constructive dismissal and sex discrimination, and is reportedly considering her legal options.
She joined Chelsea in February 2009, having previously worked at the British Olympic Medical Institute and with England Women’s Football and UK Athletics.
Meanwhile, Football Association board member Heather Rabbatts has expressed her anger at the news.
“News of Dr Eva Carneiro’s departure from Chelsea FC makes me feel sadness and anger,” said Rabbatts, who is chair of the FA’s inclusion advisory board.
“Eva was one of the few very senior women in the game, a highly respected doctor who has acted with professional integrity in difficult circumstances and whose skills have been highly praised by her colleagues, the club and governing bodies.”
The issue of team doctors has been discussed by the FIFA medical committee as a result of the incident.
Earlier this month, FA chief executive Martin Glenn said: “We work to a FIFA mandate on medical support. The duty of the doctor is to the player, not the employer. It is the Hippocratic oath. It is an issue for Chelsea to sort out but I don’t believe they are playing a dangerous game.”