The supermarket said it is the first time petrol has been sold nationally for under £1 since February 2016.
It has also cut the price of diesel to 104.7p a litre.
Ashley Myers, head of fuel for Morrisons, said: “This cut will help people who are travelling to work, those shopping for essentials, and those assisting the elderly and vulnerable.
“We want to play our full part in reducing the cost of living and feeding the nation at this difficult time.”
When one supermarket cuts petrol prices, others tend to follow so Morrisons’ move could prompt price cuts elsewhere.
The average price for fuel stands at 108.74p a litre for petrol and 114.26p for diesel, according to RAC Fuel Watch.
Experts have for weeks been calling for retail prices to be slashed further in response to wholesale fuel prices tanking as demand dried up due to the coronavirus crisis.