Kate Stone, 44, from Cambridge, was injured by the animal near Fort William in the Scottish Highlands in the early hours of Monday.
She was treated by paramedics before being taken to Fort William's Belford hospital, and later transferred by air to the Southern General in Glasgow.
A statement released by a colleague at Dr Stone's print firm, Novalia, said she had an operation late yesterday afternoon to try to repair damage to her windpipe.
It continued: "The operation went well and she remained stable throughout. The doctors made a decision to keep her in an induced coma for the next week to minimise any movement that may rupture the wound. She remains in a stable condition and she is now in the healing process from the first operation.
"Her family are with her over this new year period and all her friends are continuing to offer support."
Dr Stone was standing with a group of friends outside a private residence in Lochailort when the incident happened.
She had been on a short break at the Mo-Dhachaidh B&B in Lochailort, which is owned by Gary Burton.
Speaking yesterday, Mr Burton said the stag had panicked after becoming trapped in a fenced garden, having got through a gate.