Extra staff have now been deployed to keep the peace and a "high-level investigation" has been launched into the unrest at Moorland, Prison Service chief executive Michael Spurr said.
"We have a good record of maintaining order and security in our prisons and are therefore taking these incidents extremely seriously in order to learn lessons," he said in a statement.
The rioting broke out in the young offenders unit, housing men aged 18 to 20, on Tuesday night when about 40 prisoners refused to return to their cells after a fight broke out.
In the subsequent violence, three staff were assaulted and a female officer sustained a fractured jaw.
On Wednesday night riots broke out again, causing one prisoner to be hospitalised with head injuries. Riot officers intervened and the following day, 86 prisoners were moved to another jail.
On Thursday night the violence spread to the adult wing, and one prisoner was taken to hospital with serious injuries. Another 166 prisoners were moved to other jails in the nearby area.
Officers in riot gear were needed to restore order after at least five prison officers were injured, including a woman who suffered a fractured jaw, in the riots in Doncaster, South Yorkshire, and Woodbridge, Suffolk, which started on Tuesday night.
Almost 50 inmates needed to be transferred to other young offenders' institutions across the country after about 100 prison places were lost as a result of the damage, the Prison Officers' Association (POA) said.
About 60 offenders aged between 15 and 18 refused to return to their cells at Warren Hill, in Woodbridge, Suffolk, at about 7.30pm on Tuesday, said a Prison Service spokeswoman. Officers in riot gear, known as Prison Service Tornado response teams, entered the prison at 5.40am and the situation is now under control, she added.
"The juveniles offered no resistance and will now be relocated elsewhere in the prison estate," she said on Wednesday. "Two staff were injured in the incident. Three juveniles are being treated for minor injuries. An assessment of the damage done to the wings will be carried out later today."
The riot was prompted when a number of inmates were prevented from having free and unfettered access to the telephone and leisure facilities following incidents of alleged bullying of other juveniles, said the POA spokesman.
"They reacted with venom, causing significant damage to the prison and two prisoners being hospitalised with a number of staff injured whilst trying to deal with the riot," he said. "This is the third serious incident this year at Warren Hill which has had to be dealt with by prison officers, this time resulting in a damaging loss of prisoner accommodation."
Tom Robson, acting national chairman of the POA, said: "The level of violence in our prisons is totally unacceptable and this incident is not uncommon in our juvenile and young offender establishments. We are seeking an urgent meeting with the regional custodial manager to look at resolving these issues and preventing further violence and damage to prison property, which will all result in significant costs to the taxpayer."
In the unrelated incident at Moorland prison in Hatfield Woodhouse, Doncaster, more than 40 young offenders refused to return to their cells after a fight broke out at about 7pm on Tuesday. Tornado response teams were called in at about 1am and the prisoners "offered no resistance".
Three members of prison staff were assaulted, including a female officer who sustained a fractured jaw, and significant damage was caused to the recreation area and cells in the riot which took place during a period of association, the POA said. A number of suspected ringleaders have been segregated.