The two brothers, aged 17 and 19, were arrested after fire broke out on the second floor of the commercial building on Auburn Street about 8pm.

Cleaners who were inside the Centrelink building at the time called triple-0, the Goulburn Post reports.

Crews from surrounding jurisdictions, including the ACT, helped Goulburn firefighters extinguish the fire but not before it gutted the Centrelink office and spread into the charity store.

Firefighters were also called to a second fire at the vacant St Patrick's Primary School 200 metres away about the same time. The former school sustained minor damage but NSW Police could not confirm the two fires were linked.

Police found a 17-year-old Goulburn boy at the old school several hours after the outbreak.

They took him to hospital suffering hypothermia and burns to his feet.

Shortly after midnight, police raided a Lansdowne Street home and arrested a 19-year-old Goulburn man.

The men appeared before Goulburn Local Court on Tuesday, charged with destroy property by fire in company, aggravated break and enter to commit serious indictable offence and aggravated enter dwelling with intent.

Centrelink and Medicare customers have been urged to use its digital services while the Department of Human Services seeks an alternate site in Goulburn.

"We are working hard to make alternative arrangements so that local residents can still access in-person Centrelink and Medicare services," a statement from the department read.

Meanwhile St Vincent de Paul Society Canberra/Goulburn chief executive, Paul Trezise has asked Goulburn residents to help them replenish winter stocks lost in the fire by dropping extra blankets, doonas, jumpers, jackets, socks and gloves to two collection points at:

Canberrans looking to help can drop items off at their local Vinnies shop.

with the Goulburn Post