Mr Field has said he regrets confronting Janet Barker and marching her away as protesters interrupted a speech by the chancellor.
He said he had been “genuinely worried” she may have been armed.
Ms Barker said she would not make a complaint to police but the MP “should go to anger management classes”.
Footage of the incident has been widely shared on social media, with several Labour politicians calling for Mr Field to be sacked.
A Downing Street spokeswoman said: “The prime minister has seen the footage and she found it very concerning.
“The police have said they are looking into reports over this matter and Mark Field has also referred himself to both the Cabinet Office and the Conservative Party.
“He will be suspended as a minister while investigations take place.”
On Thursday evening climate change protesters disrupted the beginning of Chancellor Philip Hammond’s annual Mansion House speech about the state of the UK economy.