Police have charged two men after a siege near Adelaide's Public Schools Club building during which one was shot by heavily armed officers.

A 41-year-old man from Northfield and a man of the same age from Kilburn were charged with two counts of criminal trespass and several firearms offences, including possessing a loaded firearm and a prescribed firearm.

The man from Northfield was also charged with aggravated robbery in relation to an alleged car theft at Prospect on May 31.

Both men will appear in the Adelaide Magistrates Court on Monday.

The incident began at 5:15am (CST) when an alarm was activated at a real estate business alongside the club near the intersection of East Terrace and Carrington Street.

Public Schools Club chairman John Hepworth said a man a with gun was seen by those staying overnight in the club's accommodation and police were phoned.

Police evacuated a couple from the club but the secretary remained inside.

The secretary spoke with Mr Hepworth and told him a gunman on the roof of a real estate business had been shot in the arm by STAR (Special Tasks and Rescue) Group police officers about 10:10am (CST).

Police confirmed the man from Northfield was shot and wounded by STAR Group officers in the left side of the upper body and received injuries not thought to be life-threatening.

Police said he had a loaded sawed-off shotgun but a police spokesman would not say who fired the first shot or if the man fired on police.

"During the morning, while STAR Group officers were securing the external premises, there was a confrontation on the roof. At least two shots were fired," he said.

Police declared it a "significant incident" and said an investigation would take place to identify who "fired which shots".

Second suspect found hiding upstairs

The second suspect was found hiding upstairs just before 4:30pm (CST).

The police spokesman said he was found without a firearm.

Another sawed-off shotgun was earlier found in a car parked in laneway and believed to be linked to the two men.

Police earlier tried to negotiate with the men using a megaphone.

A police helicopter and police dogs were also deployed.