Police have announced an arrest after a man shouted Islamophobic comments outside the Al Noor Mosque in Christchurch yesterday.

Photo: NZ Police

A 33-year-old man is to appear in the Christchurch District Court tomorrow.

The man was wanted by police and earlier today the Police Minister Stuart Nash called on the apparent Trump supporter to hand himself in.

A social media post on a Christchurch page for members of the Muslim community showed police officers watching a man in a black T-shirt emblazoned with "Trump for New Zealand".

The post said the man was swearing and making anti-Muslim comments.

The incident occurred about 4.30pm yesterday at the mosque in Deans Avenue in central Christchurch where 42 people were killed during the terror attacks three weeks ago. The attacks also left eight others dead and dozens more injured.

"He was there for about 15 minutes, he also kicked and tried to damage some of the memorial items along Deans Ave in front of the masjid," the post said.

"The police officer who was there let him go (claiming that he can't arrest him because he didn't break any laws), and afterwards the superior officer came on the scene and said they were trying to find him to arrest him," the post said.

The police officer who failed to arrest him is no longer working in Christchurch due to a formal complaint about the incident.

A man who witnessed the anti-Muslim tirade, Adrian, said he had laid an official complaint over the police letting him walk away.

He said the man had been saying all Muslims were terrorists and needed to get out of New Zealand.

The man was spoken to by armed officers guarding the mosque, but Adrian says he was surprised and disappointed to see him let go.