They said the woman, posing as a health worker, came near the mother's bed and took the baby away under the pretext of administering immunisation drops. Since she did not return for long, the lady raised an alarm.
Hospital authorities launched a search, but in vain.
Police rushed to the spot and examined the CCTV footage, which showed the woman carrying the baby and going out of the hospital.
The 23-year-old women from Tirumarugal village had given birth to the baby girl a few days ago.