The decision to shift the prisoners was taken at a meeting at the Home and Tribal Affairs Department of Balochistan.
Senior officers from the home and prison departments attended the meeting which discussed possible attacks on prisons in the province, Dawn online reported.
Muhammad Asif Butt, superintendent of Quetta district jail, told reporters that all 24 high profile prisoners were shifted to Central Jail Mach amidst tight security.
He said Frontier Corps, Balochistan Constabulary, Police and Rapid Response Force personnel were deployed around the jail to avoid any untoward incident during the shifting.
"All prisoners have been sentenced to death," he said.
There are 97 prisoners who have been awarded the death sentence. Fourteen prisoners have filed mercy petitions before president Mamnoon Hussain.
"Within a few days, the fate of prisoners would be decided," a home department official said.
The number of inmates in all 11 jails in Balochistan is more than 3,000. According to sources in the prison department, four jails - Quetta district jail, Khuzdar, Gadani and Mach - have been declared sensitive.
Security around jails has been beefed up after the lifting of the moratorium on the death penalty by the federal government.