He slit his throat with a shaving blade at around 2AM, they said, adding that the incident came to light when night beat guards were on their rounds near his cell.
Jaishankar was first shifted to the jail hospital and later to the state-run Victoria hospital in the city, where he succumbed to injuries around 5:15 AM.
Jaishankar, who made a sensational escape from the high security central prison on September 1, 2013, wasarrested a couple of days later.
Jaishankar had committed crimes in both Karnataka and neighbouring Tamil Nadu.
He hailed from Kanyapattanam Konasamudra village in Tamil Nadu's Salem district.