Authorities deployed several hundred National Guard troops and police to help put down the riot, an AFP photographer at the scene said.
The violence broke out at the facility in the Black Sea port city as authorities planned to move several convicts to a different prison, officials said, adding that the situation was now under control.
Prisoners "attacked and wounded seven employees" and set alight a fire engine and several areas including the prison library, Ukraine's prison service said.
Ruslan Forostyak, a regional police spokesman, told AFP that the rioters barricaded themselves inside their living quarters.
The country's rights ombudswoman, Lyudmyla Denisova, said the rioters also took three medics and three guards hostage, but later said on Facebook,"they have been freed".
"The situation is under police control right now," she said.
At least six men who had arrived at the scene to support the prisoners were detained, according to the AFP photographer.
A law enforcement source source told local media that one of the reasons for the riot was the poor quality of food.
- Prison squalor -
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Established in the 1960s when Ukraine was part of the Soviet Union, the prison, Penal Colony No. 51, can hold up to 1,500 convicts.
Largely inherited from the Soviet era, Ukraine's prisons are notorious for their squalor. There are currently 57,000 inmates in around 140 prisons.
The historic port of Odessa is a multi-ethnic city of just under one million people.