The supermarket said this is the first time the fuel has been "sold nationally" for less than £1 per litre since February 2016.
It has also cut its diesel price to no more than 104.7p per litre.
Morrisons' head of fuel Ashley Myers 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."
Government figures show the average cost per litre and petrol and diesel on May 4 was 107.6p and 114.9p respectively.
The price collapse means filling a 55-litre family car is around £7 cheaper than seven weeks ago.
The reduction in the cost of fuel has been driven by a collapse in oil prices due to lower demand as global economies shut down because of the coronavirus pandemic.
Brent crude oil was trading at around 64 US dollars per barrel at the beginning of the year but sunk to under 19 dollars last month.
The price hovered around 31 dollars per barrel on Monday morning.
The number of UK motorists taking advantage of cheaper fuel is limited because the Government has restricted the reasons why people are allowed to leave their home.
Department for Transport figures released last week showed that road traffic was around 58% lower than in early February.