David Mayo said the fighting was still going on and urged the army to be withdrawn.
Local community leaders confirm that the hospital in the village of Lorema, Eastern Equatoria state, was attacked.
But the state governor’s office has denied the reports.
It says the army was sent to protect the civilian population.
‘Indiscriminate shooting’
The soldiers were deployed after eight of the governor’s bodyguards were killed when they were sent to track down cattle rustlers.
The BBC’s Nyambura Wambugu in South Sudan says many residents of the mountainous area around Lorema are heavily armed, including with rocket-propelled grenades, left over from the two-decade civil war against the north.
Mr Mayo said that 13 soldiers were currently being treated in hospital, in the state capital, Torit.
But he blames the soldiers for the violence, saying they opened fire indiscriminately when they arrived in Lorema, before going on to attack the hospital and set fire to local homes.
One doctor, one patient and four nurses died, he said.
Human rights groups have accused South Sudan’s army, made up of former rebels, of committing numerous abuses against civilians since independence in 2011 – charges the army has strongly denied.
Our reporter says there is a long history of cattle raiding in Eastern Equatoria, as in many other parts of the country.
Cattle lie at the heart of life for many communities in the country which has hardly any banks – they represent wealth, a dowry, property and a source of food in the lean season.
A single cow can be worth hundreds of dollars depending on its colouring.