Robben, 21, sustained a broken foot in last week's Premiership match against Blackburn and Mourinho is believed to have told the club doctor Neil Frazer that he had to get the player fit for the Carling Cup final against Liverpool on 27 February.
When Frazer told Mourinho that the player would not be fit in time, he is understood to have been told by the Portuguese coach that he was no longer wanted at the club.
For the first time this season, Mourinho is facing an injury crisis with striker Didier Drogba, defender Ricardo Carvalho and Robben all struggling for fitness. The Chelsea coach made just one signing, Jiri Jarosik, during the transfer window.
Chelsea issued a statement last night, saying: "Dr Neil Frazer has stepped down from his position as club doctor due to ill health after nearly four years with Chelsea. The club would like to thank him for his service and wish him all the best in the future."
Robben, the winger so influential in Chelsea's rise to the top of the Premiership, described his foot injury as "a disaster" after scans revealed he had broken two bones. The Dutchman could be out of action for up to two months before he is ready to rejoin the club's quest for the title.
Robben said: "This is a disaster. Everything was going so well. It is a massive blow and comes just at the moment when I was in top shape."
The 21-year-old missed the first two months of the season with a broken bone in his other ankle.
The Netherlands coach Marco van Basten has warned Robben that he must learn to tackle differently if he is to stay clear of the foot injuries which have taken the shine off his successful first season with Chelsea.
Van Basten, whose career was ended by an ankle injury at the age of 29, said: "Every defender knows they must eliminate Robben. Maybe he must learn to go differently, more light-footed into a duel. I had to do that in the past. That is something he'll learn."