The M25 was closed between junctions six and seven in Surrey on Monday morning after a protester from the anti-fossil fuel group climbed an overhead gantry.
A protester also targeted junction 30 of the major motorway circling London, with Essex Police urging the public “not to intervene”.
Surrey Police said the decision was made to close the road “for the safety of everyone” while officers attempt to remove the activist, while Essex Police said it was “dealing robustly” with the issue.
Mr Shapps, the business secretary, said it was “completely outrageous” for activists to disrupt traffic – referring to prison sentences handed to fellow climate activists who previously blocked the M25.
“When I was transport secretary, I made sure National Highways used injunctions and quite a number of people from one of their sister organisations spent this Christmas in prison – I hope that’s what happens here as well,” he told LBC.
Mr Shapps said: “I have no issue with people arguing for lower levels of petrol, of gas or whatever other thing they want to campaign for. That is one thing … There are perfectly legitimate ways to campaign on climate change.”
He added: “But don’t go disrupting people’s lives. It’s unacceptable. It’s illegal. It’s completely wrong to disrupt people’s lives this way … I hope that justice is served up to these people.”
It comes after police made a series of pre-emptive arrests ahead of planned action by the Just Stop Oil group on the M25.
National Highways secured a High Court injunction to stop the protesters disrupting from any unlawful demonstrations disrupting England’s busiest motorway.
Surrey Police tweeted said officers were dealing with a protester who managed to climb onto the motorway gantry at junction 6 towards 7 of the M25 – shut the road from those junctions northbound on the motorway.
A Just Stop Oil protester also targeted junction 30 of the major motorway circling London, with Essex Police urging the public “not to intervene”.
The Essex force tweeted: “Arrests have been made already. We are dealing robustly and ask the public not to intervene.”
The Metropolitan Police said three activists suspected of planning public disruption on the M25 were arrested on Sunday on suspicion of conspiracy to cause a public nuisance.
“Our investigation has strong reason to suspect the Just Stop Oil group intend to disrupt major motorway road networks which would risk serious harm to the public, with reckless action to obstruct the public on a large scale,” said assistant commissioner Matt Twist.
The latest court injunction was secured in addition to a court order obtained by National Highways earlier this year that targeted protesters including those from Insulate Britain.
It means that anyone entering the motorway and fixing themselves to any object or structure on it, and anyone assisting in such an act, can be held in contempt of court. They could face imprisonment, an unlimited fine, and the seizure of assets.
Transport secretary Mark Harper said he instructed National Highways to apply for the latest injunction, saying: “This will make it easier to take action against this reckless minority of protesters.”