Rescue teams will work into the night to try and find survivors among the rubble.
Thames Valley Police confirmed emergency services rushed to the scene after reports of an explosion at around 4pm.
South Central Ambulance Service declared a “major incident” and confirmed there could be several casualties.
An air ambulance, three road ambulances, a rapid response vehicle and a hazardous area response team were sent to the scene.
Witnesses described hearing a loud bang before parts of the building collapsed.
Another reported “loads of dust” and “loads of emergency vehicles” at the scene of the explosion.
The building was scheduled for demolition in just ten days.
Rodney Rose, deputy leader of Oxfordshire County Council, said he had been told there had been at least one death at the site.
He told a local newspaper: “I have been told there has been one fatality, but the rest is currently unknown.
“The fire service is there now and we are still trying to find out if this was a demolition.
“At the moment this is being treated as a collapsed building, not an explosion, but there was a bang.”
A police statement added: “Thames Valley Police officers are currently in attendance at Didcot Power Station dealing with an incident with other emergency services.
“Further information will be released in due course.”
Photographs from the scene showed part of a building missing, which appears to be the former coal-fired Didcot A, which closed in 2013.
The power station was earmarked for demolition but a spokeswoman for RWE NPower, which manages the site, said they were not aware of a planned demolition at the time of the explosion or any in the near future.
Eyewitness Adrian Redhead said: “I’d just got home from work just after 4pm when there was a massive noise – it sounded like a train had come off the rails.
“Sirens were all over the place. I looked outside and saw all the dust. There were loads of emergency vehicles. There are two helicopters above now…. a load of dust came over the house.
“Half of it has come down and the rest of it is hanging by a thread.”
Oxford University Hospitals NHS Foundation Trust said “casualties” were being taken to the John Radcliffe Hospital in Oxford and asked the public to stay away unless suffering “serious or life-threatening emergencies”.
A spokesman said: “Casualties are being directed to the emergency department of the John Radcliffe Hospital which has been made ready to receive them.
“We are not able to release any information on numbers of casualties at this time.
“We are grateful to members of the public for avoiding attending our emergency department for anything other than serious or life-threatening emergencies.”
Eyewitness Bill McKinnon, who lives in Didcot near the scene of the explosion, went on: “About 4 o”clock, when I heard the explosion and the very loud rumbling, by the time I had got up and looked out of the window there was a huge cloud of dust which came through and over our village.
“When that had cleared I noticed that half of the old power station, where they used to keep the generators, half of that was missing.
“There wasn”t any physical feeling, it was only noise. When they took down the cooling towers a couple of years ago it was about the same volume as that. It was quite loud.”
He added: “I was a little bit surprised because normally the contractors let us know when they are going to do explosions, so I was a bit surprised because we hadn”t heard anything.
“Very shortly afterwards the air ambulance turned up and then fire engines and ambulances started arriving, and a little while after that another air ambulance turned up, and I think they are still there.”
Mr McKinnon said the explosion took place in a large building which housed the generators for producing power.
David Cooke, whose company Thames Cryogenics have a building overlooking the power station, said it “shook”
He added: “A s we looked out of the window, the end of the main turbine hall collapsed in a huge pile of dust.
“It totally obscured the towers and must have drifted across the roads and main rail line. What”s left looks a tangled mess.
“The dust was hanging over the area for five to 10 minutes.
“First thought was, it didn”t looked planned, followed by the thought that people are going to have been hurt.”
Three enormous cooling towers at the disused Didcot A Power Station were demolished in July 2014.
A controlled blast took place with more than 180kg of explosives being used to flatten 36,000 tonnes of material in seconds.
Hundreds gathered to watch and the event was streamed online.
The blaze was described as “ferocious” but National Grid said there was no operational impact.
More to follow..