The doctors were monitoring the training session of the Scotland squad on the back pitches at Murrayfield when they were called over to help the man.
He was treated on the scene by the medics before an ambulance crew transported him to the Edinburgh Royal Infirmary.
The incident happened at round 1pm yesterday.
A spokesman for Scottish Rugby said: "A member of the public took ill at Murrayfield Stadium earlier today. He was swiftly attended to by members of the Scotland and Edinburgh Rugby medical teams before being taken to hospital. Scottish Rugby wish the individual in question a speedy recovery."
The Scottish Ambulance service confirmed that a 35-year old man had suffered a suspected cardiac arrest at Murrayfield Stadium and had been transferred to the ERI.