The incident, which took place at Wilton Terrace near the city centre of the Irish capital, happened on Tuesday afternoon.
The tent is believed to have been pitched alongside the Grand Canal, a waterway which runs through the heart of Dublin and is popular with walkers and cyclists.
It is thought the man was injured when the tent he was sheltering in was moved by vehicle during works to clear the banks of the canal.
Local police said investigations into the incident are continuing.
In a statement, Dublin City Council said the incident happened while Waterways Ireland was removing tents that it said were "placed in a precarious and dangerous location".
"An individual was injured during the process and was taken to hospital. The Dublin Regional Homeless Executive is currently liaising with the hospital and every support is being provided," the statement added.
The authority said its thoughts were with the man after his injury, adding it had been "engaging with the individual for some time" to provide him with alternative accommodation.
In comparison, figures released for London last year showed the 8,855 people slept rough in the capital between April 2018 and March 2019.