Kate Stone, 44, is in an induced coma following surgery earlier this week to try to repair damage to her trachea, or windpipe, caused when she was injured by the animal near Fort William in the Scottish Highlands.
A statement released by colleagues at Dr Stone's print firm Novalia said they had received an overwhelming number of messages of support following the accident.
Dr Stone, from Cambridge, was on a short break with friends when the stag ran towards her while she was standing outside a private residence in Lochailort in the early hours of Monday.
She was taken to Belford Hospital in Fort William before being transferred by air to the Southern General in Glasgow.
The statement from colleagues said: "Having spoken with the hospital, we understand that she will remain in an induced coma for the next few days to minimise any movement following her surgery earlier this week.
"She remains in a stable condition and the doctors are pleased with her progress so far.
"We have received an overwhelming number of messages from friends, colleagues and clients for Kate, which we are looking forward to passing on to her."