Carlos Sainz won the 2022 British Grand Prix
Several sporting events have been disrupted by climate and animal rights groups in recent months.
Stuart Pringle said "enhanced searching" may help prevent protests.
"It is a ridiculously reckless thing to put your own life at risk," Pringle said.
"[It also risks the lives] of the drivers, spectators and marshals."
He told BBC Radio 5 Live that Silverstone has an added advantage - a fence - in keeping protesters off the track.
"Unlike cricket or tennis, we have a fence which is designed to stop parts of a racing car, in the event of an accident, going into the crowd," he said.
"That is helpful but it is designed to help keep debris going in the fans, not to stop a determined person that wants to put their life at risk."
He said there would be 480,000 people attending the circuit over four days.
Just Stop Oil protestors have disrupted other sporting events such as the Ashes, Wimbledon and rugby union's Premiership final recently, while supporters of Animal Rising disrupted the Grand National and Derby at Epsom.
Supporters of Just Stop Oil were also handed suspended prison sentences and community orders after invading the Silverstone track in 2022.
Home Secretary Suella Braverman led talks with sport leaders on Wednesday to look at how they could tackle disruption.
Speaking about that meeting on Thursday, policing minister Chris Philp said sports were being encouraged to hire more marshals and use injunctions to prevent protests.
"We'd like to see obviously those sporting organisations increase the number of marshals and stewards. They have to be more careful about checking people coming into sporting events and react really quickly when something happens," he told Times Radio.
"At the meeting yesterday we had with sporting leaders we encouraged the use of injunctions because that allows for a much more severe criminal penalty if the injunction gets breached."
Pringle agrees tougher stances are needed, and pointed out there would be "enhanced searching" in operation for those attending the race weekend.
"I think we need stronger sanctions," he said.
"The people who invaded our track last year were given suspended prison sentences, how that is appropriate I have no idea.
"They were grossly putting people's lives at risk - their own and spectators', marshals' and competitors'.
"I hope there might be a more robust approach to that. It is an offence to run on to a football field, I don't understand how it is not an offence to run on to a cricket pitch or a tennis court.
"But if you run on to Silverstone this weekend it will be aggravated trespass and that is a criminal offence."
--- Courtesy of BBC Sport