Two supermarket delivery vans were torched less than an hour after Prime Minister Boris Johnson issued his lockdown order.
Patrolling officers came across the Iceland vans alight in Southmead, Bristol at about 21:30 GMT on Monday.
It was "beyond belief anyone would be so reckless and thoughtless", Avon and Somerset Police said.
Iceland said it was "shocking anyone would act so callously" when the vans were "most needed".
The vans were set ablaze deliberately, Avon Fire and Rescue Service believe.
Ch Insp Mark Runacres said officers were already on patrol in the area following "recent instances of anti-social behaviour".
"We put an order in place last night to give officers extra powers to disperse groups and will continue to use our existing powers to tackle this problem," he said.
"We believe that a group of teenagers were involved in these disturbances. I have one message for them, their parents and carers. 'Stay at home. Save lives'."
A spokesman for Iceland said "both vans would have to be written off".
"While we can and will bring in replacement vans to maintain our home delivery service in Southmead, our entire van fleet is running at absolutely full capacity at the moment," he said.
"And it is shocking and distressing that anyone would act so callously to put vehicles out of service at precisely the time when they are most needed to deliver food to the most vulnerable people in our society."