New Zealand police have arrested a man wanted over a fatal double shooting at a social security office on the South Island.

Police had been looking for the man since the shooting this morning, which left two people dead and another seriously injured.

A witness said the gunman opened fire on staff in the Ashburton branch of the Work and Income office before escaping on a bicycle.

Police said the suspect, named earlier as 48-year-old John Henry Tully, was bitten by a dog as he was taken into custody.

Canterbury District Superintendent Gary Knowles said the Armed Offenders Squad and teams from Christchurch and Ashburton police were involved in the search for Mr Tully.

It is believed Mr Tully was known to employees at the Work and Income office.

The shooting prompted the ministry of social development to close all its offices near Ashburton.

"We are all shocked by the news of this morning's incident," chief executive Brendan Boyle said in a statement.

"What I can say is that we will be there for our colleagues to support them as they come to terms with what has happened."

New Zealand social development minister Paula Bennett is due to arrive on the South Island to meet with social security staff who were caught up in the deadly shooting.

Mr Tully is understood to be on a disability pension and reportedly told a local newspaper he had come home to die from an unidentified skin disease.