The men used bedsheets tied to broom handles to flee through the window of Rome's Rebibbia prison in the early hours of Thursday morning, Repubblica reported.
The three were among 39 inmates of Camerino prison who were moved to the Rome jail last night. The prison, along with local hospitals, university residences and care homes, was evacuated as central Italy suffered a series of destructive earthquakes.
One of the men was serving a life sentence for murder, arms trafficking and involvement in a prostitution ring, while another was due for release in 2041, having been found guilty of attempted murder, and drugs and arms trafficking. The third was serving jail time for pimping and drugs trafficking, with his sentence set to end in 2020.
By mid-afternoon on Thursday, the inmates had still not been tracked down. Repubblica has shared police images of the three escapees.
But due to the move, they were housed in a lower security area of the Roman prison, usually reserved for inmates convicted of more minor crimes.
Knotted bedsheets are a fairly common escape tool in Italy's prisons.
Two men jailed for robbery used the same method to escape from the Rome jail in 2014. That escape had been the first from Rebibbia in 20 years - however jailbreaks had also occurred at other prisons across Italy.
Earlier that year, for example, a prisoner in Sicily broke the bars of his cell at Pagliarelli prison and climbed down the wall on a rope of knotted sheets. The same man had managed to escape from a prison in Parma a year earlier.
And in February 2016, the same technique was used by another convicted killer serving time in Rebibbia, who escaped along with a fellow inmate, prompting a national manhunt.