Owners EDF said the power station suffered an industrial incident in the form of a 'steam release', which caused a blast of high-temperature steam to escape at 10.30pm on Monday.
Two of the casualties were taken to Royal Preston Hospital, Lancashire's major trauma unit, and a third person was taken to Wythenshawe Hospital in Manchester.
All three male casualties are EDF employees.
An EDF spokesman said the incident was 'not nuclear related' and did not pose a threat to the public.
The spokesman said: “Emergency services attended Heysham 1 power station following an incident at the site on the evening of Monday 19 November.
"The three colleagues who were injured have been taken to hospital where they are receiving treatment for their injuries – two at Preston and the other at Wythenshawe.
"It goes without saying that everyone’s thoughts are with our three colleagues who have been injured, and we will be doing everything we can to support them and their families while they recover.
"There was no risk to the public during the incident which is now under control.
"A full investigation into the cause will be carried out. Safety is our overriding priority and we will investigate how this happened and make sure all measures necessary are put in place to ensure it doesn’t happen again. “
She added: "This is not a common occurrence, and we do regard it as a serious incident due to the injuries to the three people on site.
"But we do plan for these incidents and we have an emergency response team prepared for these types of incidents."
EDF declined to comment on the extent of the injuries sustained in the incident.
Fire crews from Morecambe, Bolton-le-Sands, Bispham and South Shore in Blackpool were called to the scene after an automatic emergency alarm was sounded.
The incident was managed by the power station's emergency response team, with five fire crews from across Lancashire remaining on standby at the site.
Heysham 1 suffered a major incident in 2015, when a significant CO2 leak affected the same nuclear power station. There was no immediate nuclear safety or radiological risk as a result of the event, but the government's nuclear watchdog, the Office for Nuclear Regulation (ONR), warned that the incident "could have had serious implications if workers had been in the vicinity, including potential fatalities".
On March 16, 2015, a failed pipe at the Heysham facility released approximately 30 tonnes of clean Carbon Dioxide (CO2) into the atmosphere.
The ONR said it highlighted a "failure to adequately maintain the Carbon Dioxide storage and distribution system", which provides the coolant gas for the Heysham 1 reactors.
The government's report said: "Although no one was injured, CO2 is a substance that can be hazardous to health and the quantities released could have had serious implications if workers had been in the vicinity, including potential fatalities."
"ONR immediately commenced an investigation into the event and, on 25 March 2015, served an Improvement Notice on NGL for its failure to maintain its Carbon Dioxide storage and distribution plant at Heysham 1 power station."
The ONR said it is aware of the incident at Heysham last night and will release a statement later today.