From late January, the grocer will instead label 90% of its own-brand milk with "best before" dates and encourage shoppers to sniff for quality.
The move, the business claims, will save millions of pints of its own-brand milk every year.
Morrisons is the first supermarket to announce the change, claims Wrap.
"Wasted milk implies wasted effort by our farmers and wasteful carbon emissions," said Ian Goode, Morrisons' senior milk buyer.
"We believe that good quality milk should be eaten rather than thrown away after its "use by" date."
So, today we're taking a risk and asking customers if their milk is still safe to drink.
"Previous generations employed the sniff test, and I believe we can too."
A sour fragrance or curdled consistency indicates spoilt milk.
According to Wrap, about 490 million pints of milk are thrown away every year in the UK, behind potatoes and bread.
Customer's obeying "use by" labels even though study shows product can be utilised days after the date.
"I am happy that Morrisons is the first UK supermarket to adopt this critical step to help decrease domestic food waste - it shows real leadership," said Wrap's Marcus Gover.