The MP from Vijayawada was arrested by the police and shifted to the hospital from the hunger strike camp.
According to police, as the hospital staff were making arrangements to shift him to a private hospital, he walked out with a friend and disappeared.
Eye-witnesses said Rajagopal came out of the hospital at around 10.10 pm with his friend and driver and sped away in a vehicle even before policemen deployed there could understand anything.
The MP, who was fasting for last six days, was unhappy with the central government for not withdrawing its statement on formation of Telangana state.
The state government had also rejected his demand to shift him to Nizam's Institute of Medical Sciences (NIMS) in Hyderabad.
Police went on high alert in Vijayawada and launched a large scale search for the missing MP as he might try to make dramatic appearance here to lodge his protest.