The doctor attacked the woman in the secluded intensive care unit of the hospital in Ahmedabad. Another hospital worker has also been arrested for allegedly helping the doctor carry out the crime.
Police said the doctor gave the patient strong drugs to make her unconscious, before raping her.
The doctor is a Pakistani national who has been working in India on a long-term visa since last year.
The Apollo Hospital said it was fully co-operating with the police, and since the investigation is ongoing they do not want to comment on the incident.
Sadly, rape and gender crimes have been in the spotlight in India in recent years, and continue to be reported across the country.