Motorists are exploiting quieter than usual roads to drive at "highly excessive speeds", police have warned.
People across the UK have been urged to stay at home unless absolutely necessary to slow the spread of coronavirus.
North Yorkshire Police said it believed less traffic meant some drivers and motorcyclists were flouting the law.
It urged people "not to tie up valuable police or NHS resources by committing dangerous but preventable offences".
Assistant Chief Constable Mike Walker said: "These actions can have fatal consequences which tie up emergency services."
As well as speeding, officers have also reported seeing more drivers committing offences including mobile phone use, drink or drug-driving and not wearing a seatbelt.
Mr Walker said: "While many people are following the very clear government advice to stay at home and only make essential journeys, sadly we have seen some motorists using the roads irresponsibly, with highly excessive speeds recorded on key routes and other dangerous offences.
"These actions can have fatal consequences which tie up emergency service and medical resources at a time when they are needed most.
"We have a duty to uphold the law and keep our roads safe for everyone, regardless of the wider situation nationally."
He said those caught breaking the rules would be dealt with accordingly.
However, he added: "Let me be very clear - motorcyclists and drivers should be staying at home unless their journey falls into one of the essential criteria outlined by the government."