The inmates had launched protests amid a surge of coronavirus infections in the prisons, demanding early release on bail and better facilities.
Police spokesman Ajith Rohana said guards had "used force to control an unruly situation" in the Mahara prison.
Around 1,000 cases have been reported from the country's overcrowded prisons.
Media reports say prison guards had opened fire to contain the riot. Local news reports quoted residents who said they had seen a "massive fire" on the premises.
Deputy Inspector Ajith Rohana told BBC Sinhala that the injured had been admitted to the local Ragama hospital.
Mr Rohana added that a contingent of elite police commandos had been called to tighten security around the prison, and five police teams had also been deployed.
This is the latest in a series of prison riots that have taken place in Sri Lanka in recent weeks, as the number of Covid-19 cases in jails continues to increase.
In the capital Colombo, a group of protesters at Welikada jail launched a protest on the top of a prison roof asking that they be granted bail.
Inmates protested on the top of the prison building in Colombo/REUTERS
Another group of inmates at the Angunakolapelessa prison have been protesting for eight days, alleging that conditions in their prison have worsened.
Rights groups say some 26,000 people are housed across facilities that have a capacity of about 10,000.
Sri Lanka experienced a surge in virus cases last month when two clusters - one at a garment factory and another at a fish market - emerged last month.
According to Johns Hopkins University, there are now 23,484 cases in Sri Lanka with 116 deaths reported. (BBC)
