It happened at HM YOI Aylesbury in Buckinghamshire on Friday morning, Thames Valley Police said.
An online prison blog said 30 inmates took part in the "mass brawl".
Police said the injured people had since been released from hospital. The Prison Service said it was investigating the incident with police.
Officers were called to "a report of disorder" at the young offender institution in Bierton Road at about 11:00 BST, but "officer deployment was not required at the incident", a spokeswoman said.
"Seven prison officers and one prisoner were taken to hospital for treatment."
The incident came to light in an online blog on Prison UK.
Author Alex Cavendish, a former prisoner, said he was passed the information via "reliable, professional sources inside the system".
"A mass brawl broke out yesterday morning... Prisoners were attacking each other with weapons - and staff," the informant said.
He described the incident as "horrific".
"Staff were trying to save their lives and got battered. Some were seriously injured. Another officer was on the landing unconscious.
"We had ambulances and fire service in, trying to help alongside our healthcare department.
"The wing has been brewing for a while," he added.
A Prison Service Spokesman confirmed that "an incident involving a number of prisoners took place on Friday 21 July".
"We do not tolerate violence against our hard-working staff. Where incidents like this occur, we will always work closely with the police to push for the strongest possible punishment," he added.
The incident is being jointly investigated by the Prison Service and Thames Valley Police.

At a meeting in Australia, it was agreed that around 1.5 million sq km of a part of the Southern Ocean would be protected from companies wanting to fish there for the next 35 years.
The Ross Sea actually only makes up about 2% of this ocean, but it is home to a huge amount of wildlife.
Environmental campaigners have welcomed the decision saying it will help to protect Earth's cleanest area of ocean.
They hope it will be the first of many such zones across the world.
You will find around two in every five of the world's Adelie penguins here, around one in three Antarctic petrels and around one in 16 of the world's minke whales. Killer whales live there too.
It is also a rich source of krill, which is food for seals and whales, so it's very important that it is looked after.
Here are 10 things you probably didn't know about Antarctica...
Antarctica isn't a country - it's a whole continent!
It is sits at the Earth's south pole and is almost completely covered by an massive ice sheet that is thousands of metres thick.
Antarctica is absolutely enormous. It is almost 14 million sq km, which makes it the fifth-largest continent behind Asia, North America, South America and Africa.
This is about 58 times the size of the UK and twice the size of Australia!
It is also the world's highest continent, with an average land height of 2,300 m.
The temperature on Antarctica has been known to go as low as around âˆ’90Â°C.
Because it is so cold, the air cannot hold as much moisture so it does not rain very much at all there.
This actually means Antarctica is considered to be a desert, but the other deserts that you know are much warmer...!
The winds can always blow as strongly as up to 351 km per hour.
As it is such an important place for scientific research, at any one time there may be many hundreds scientists spread across the various research stations all over the continent.
You will also find tourists there. According to Discovering Antarctica, in the early 1990s, about 5,000 tourists went every year. By 2009-2010, the continent welcomed around 37,000 visitors.
But nobody lives there permanently!
In the winter, the sea around Antarctica freezes over creating what is called sea ice. This makes the continent almost twice as big in winter.
The end of the summer in Antarctica is in March and the end of the winter is in September - opposite to in the UK!
This is because Antarctica is in the Southern Hemisphere, which faces the Sun during our winter time.
In 1959, several countries signed an agreement called the Antarctic Treaty, saying that Antarctica would be a peaceful place that they would work together to look after.
Without an international agreement like this, people would be free to do what they wanted there. However, this meant countries now work together to protect it.
Seven prison officers and one prisoner were taken to hospital after "disorder" at a young offender institution, police have said.
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Officials from 24 countries and the European Union have agreed that the Ross Sea, in Antarctica, will become the world's largest marine protected area.