She was speaking after DUP MP Carla Lockhart again called for Ms O’Neill to go following the Drumcree dispute.
Ms O’Neill, along with Sinn Féin president Mary-Lou McDonald, a number of senior party members and People Before Profit MLA Gerry Carroll, was questioned by police probing potential breaches of a Parades Commission determination to allow an Orange Order parade along the Garvaghy Road in Portadown.
The move sparked fury among nationalist residents of the road after the route got the green light for the first time in almost 30 years since the flashpoint saw significant disorder in the 1990s.
Large-scale protests on the Garvaghy Road effectively prevented the Orange Order parade from being able to complete its traditional route.
On Saturday night, thousands of people lined the streets of Portadown in support of the Orange men.
Local MP Ms Lockhart addressed the crowd, telling them “profound consequences must mean profound consequences. Michelle O’Neill must go”.
“That’s where I stand and this lady is not for turning.”
This was greeted by boos throughout the crowd, along with chants of “the first minister has to go”.
Ms Lockhart resigned as a DUP party officer last week in a deepening row with the leadership over the future of Stormont.
The move came amid a difference of opinion between Ms Lockhart and DUP leader Gavin Robinson on whether the party should withdraw deputy First Minister Emma Little-Pengelly from the powersharing executive.
Speaking to media in Belfast on Monday, Ms Kimmins responded by saying: “Michelle O’Neill is going nowhere.”
“The people decided who the First Minister of the north is and that’s the way that will remain,” she said.
“Carla Lockhart and whoever else can say what they want, but the facts remain democracy is who elects the First Minister. Michelle O’Neill is going absolutely nowhere.”
Ms Kimmins also confirmed that she has received a letter from police inviting her for interview in the Drumcree investigation.
She declined to say when she will attend that interview but added she will co-operate with the PSNI as required.