In a third detention facility, officials used tear gas to control inmate protests.
Public Security Minister Ananda Wijepala told parliament on Friday that one inmate died at Colombo Magazine Prison in the capital, Colombo, late on Thursday when about 40 prisoners clashed after breaking out of their cells.
Two inmates died Friday morning at Kuruwita Prison in Kuruwita town about 80km from the capital, Wijepala said.
Between the two incidents, 23 inmates were injured and admitted to hospitals, Wijepala said, adding that the violence was related to narcotics dealers and rival criminal gangs.
Prison officials could not immediately be reached for comment.
Separately, prison officials used tear gas to control inmate protests at the Pallansena Correctional Center on Friday.
There were no immediate reports of casualties.
The reports of the three deaths come a month after a clash in Negombo prison on July 6 left at least 26 people dead including seven prison officers.
Sri Lankan prisons are highly congested, with more than 39,000 inmates crowded into a system with a total capacity of just 10,000, according to a recent speech in parliament by Justice Minister Harshana Nanayakkara.
"The number of prisoners in Sri Lanka today is four times the capacity," said Senaka Perera, president of the Committee for Rights of Prisoners.
"In fact, they have been patient for so long."
A large number of jail inmates are suspects awaiting trial for alleged narcotics-related offences.
Recent laws tightening bail conditions had resulted in prison overcrowding, Perera said.
The poor living conditions in the congested prisons keep inmates in constant agitation, which triggered incidents, Perera said.
His organisation has made numerous pleas to authorities to categorise drug addicts as medical patients and establish separate rehabilitation facilities, Perera said.
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