Police were called to the Parap shopping centre in Darwin about 4am on Tuesday after reports a man had broken into the Fannie Bay MP's office and caused extensive damage.
Officers took a 47-year-old man into custody, saying the matter was under investigation. He is expected to be charged later on Tuesday.
Mr Gunner confirmed his office had been targeted.
"My electorate office was broken into at 4am this morning," he said on Facebook.
"It was a very personal break-in targeting photos of me and items of personal importance to me.
"My staff are OK, my family are OK ...We'll take advice from police on what our next steps may need to be to keep my family safe."
The current chief minister, Natasha Fyles, said it would be "extremely disappointing" if the break in was found to be a personal attack on Mr Gunner.
"Michael put his hand up and served our community for 14 years," she told reporters.
"He deserves now to spend time with his family and feel safe doing so."
Mr Gunner on Wednesday announced he was quitting NT politics, forcing a by-election that is scheduled for August 20.
The 46-year-old had been on the backbench since May when he resigned from the top job, saying his head and heart were no longer in the role.
Anti-COVID-19 vaccination protesters allegedly made several death threats against Mr Gunner and his family late in 2021 after the government announced vaccine mandates for workers.
Mr Gunner remained a target after he resigned from the chief minister's role, with protesters confronting him and his family in social settings around Darwin.
He first won the Fannie Bay seat in 2008 and was returned by a margin of more than 800 votes at the 2020 territory poll.
