The MP, whose Eastwood seat, near Glasgow, is the Conservatives' safest in Scotland, was taken by ambulance from his home in Neilston near the city shortly before 6pm.
In a statement, the deputy chairman of the Scottish Conservative Party, Annabel Goldie, said: "We understand that Allan Stewart suffered a deterioration in health and as a consequence has been admitted to hospital.
"We are obviously deeply saddened by the news and our thoughts centre solely on his wife Susie and the family and we would urge that they be given peace and privacy to help them through this very difficult time."
A spokesman for Dyke Bar Psychiatric Hospital, less than five miles from Mr Stewart's home, would not confirm reports that the MP had been taken there.
The spokesman, Paul Mortimer, said: "We do not make any comment on whether or not any individual is a patient within the hospital.
"Nor would we make comment on any individual's condition, should they be a patient in the hospital."
Other hospitals in the city denied that the MP had been admitted to their wards.
Mr Stewart, 51, resigned on Monday, saying press reports about his health and personal life had caused "great family distress and personal strain".
At the weekend, a Scottish newspaper linked his name with a married woman he was said to have met at a clinic in the Borders, specialising in alcohol problems.
In a letter to his local Conservative association chairman, Ian Muir, Mr Stewart said that after discussing his position with his wife, Susie, he had decided to resign.
Mr Muir described him as a man of "sensitivity, which meant he took the knocks harder than some and which, in the final analysis, took its toll of his health and, on occasion, his judgment".
The Labour Party's Scottish spokesman, George Robertson, said he was "shocked and deeply saddened" at the news that Mr Stewart had been admitted to hospital.
The local party selection committee has reviewed applications and will conduct interviews over the weekend. It will then submit a shortlist to the Eastwood party executive, expected to meet early next week.