The brothers were arrested after a blaze ripped through the Centrelink building in Auburn St just after 8pm, causing chaos for two government departments and destroying a charity shop.

At the back of the Cartwright Place building, a smaller fire erupted at the same time in insulation batts and timber allegedly pushed into a corner at the former St Patrick's Primary School site.

Several hours later, investigating police found a teenager inside and arrested him.

He was hauled from the building wearing a breathing mask, suffering smoke inhalation, burns to his feet and hypothermia.

The teen was taken to Goulburn Base Hospital for treatment before being taken to the local police station.

At about 12.30am Tuesday, acting on information, police searched a Lansdowne St home and arrested his 19-year-old brother.

Forensic services removed several items for examination, the Post observed.

The pair were charged and bail refused by police overnight.

The teenagers, both from Goulburn, each faced counts of destroying property in company using fire, aggravated breaking and entering in company; and aggravated entry of a dwelling.

Police said that between 8pm and 10pm on Monday, the pair intentionally or recklessly destroyed the Centrelink/Medicare office in Auburn St.

Officers also alleged the duo intentionally or recklessly destroyed part of 57 Verner St that was being renovated.

The 19-year-old appeared in the dock with bare feet and head bowed.

His solicitor did not apply for bail and it was formally refused by Magistrate Carolyn Huntsman.

The 17-year-old appeared in Goulburn Children's Court.

He also appeared in the dock with bare feet.

His solicitor did not apply for bail and it was also formally refused.

The pair did not enter any pleas and all matters have been adjourned to Goulburn Local Court on August 10.

The northbound lane of the block remained closed to traffic but police hoped to open it later this morning.