They were working at Thomond Bridge in Limerick when the incident happened at about 15:30 local time on Saturday.
It is understood the men were wearing safety harnesses to tether them to a cage, suspended from a crane, when it broke away and fell into the River Shannon.
A third man who was working with them is believed to be unhurt.
He managed to free his harness and swim down river but the two others were trapped in the cage.
The two men who died, aged in their late 20s and early 40s, are thought to have been underwater for about eight minutes.
Rescuers freed the men from their harnesses and brought them ashore.
Rescuer Tom Cusack said he saw one of the men "floating down the river" when he arrived at the scene.
"We took him into the boat and he informed us that two of his colleagues were trapped underwater in this cage," he said.
"We continued on up to the location, the cage was just maybe two feet underwater, and the two men were trapped inside."
They were taken to University Hospital in Limerick, but were later pronounced dead.
Limerick City and County Council said the men who were employees of a firm contracted to carry out repair work to the bridge.
In a statement, the council said it was working with Irish police and the Health and Safety Authority, and expressed its sympathy to the families and colleagues of the men.
Two men have died after falling from a bridge in the Republic of Ireland while carrying out maintenance work.