The disorder at HMP Erlestoke began on Saturday when two inmates escaped their cells and threatened staff.
No-one was hurt and those involved in the incident are being investigated by police, the Ministry of Justice said.
The Prison Officers' Association said the issues surrounded a lack of regime due to insufficient staffing levels.
A Ministry of Justice spokesman said "two separate incidents" involving three prisoners had been "successfully resolved" on Saturday.
He added the prison was now "running as normal" and said there had been "some minor structural damage".
He said: "We are absolutely clear that prisoners who behave in this way will be punished and can spend significantly longer behind bars."
The Prison Officers' Association (POA) said order was restored overnight on Saturday but said "both wings were destroyed and were now out of commission".
The POA spokesman added this was "another example of a failed benchmark process brought about by savage and unnecessary government cuts that has seen staffing levels decrease to an unsafe level".
Relatives of inmates also got in touch with the BBC saying prisoners were kept locked in their cells for three days, without hot food, hot water and no prison officers on some wings.
Conservative MP, for Devizes, Claire Perry said: "I was saddened to hear of the disturbances at Erlestoke Prison over the last few days.
"These incidents are wholly and utterly unacceptable, and I understand that these matters have been referred to the police to consider charges against the perpetrators."
A disturbance at a prison saw 130 inmates transferred to nearby jails after two wings were put "out of commission", a union has said.