The latest move comes on top of the 2p/litre price cut the company said it would be imposing just two weeks ago.
This will bring its standard litre price down to just 20.75p/litre from 1 May 2020, according to a letter sent to its suppliers on Wednesday (15 April).
The letter also said payment delays will now be extended by a further seven days to three weeks overdue, meaning farmers will not be receiving their 13 April payment until 4 May.
A company statement said the changes were “regrettable” and related directly to the impact of the coronavirus pandemic on its core revenues from the food service and wholesale market sectors.
Arfaiz Hussain, Medina’s director of processing, said: “Since my last communication the situation for us and [the] UK milk industry has deteriorated rapidly.
“The loss of food service sales, together with the first signs of the spring milk flush means that there is just too much milk!”
Mr Hussain pledged that the company would continue to collect all milk and not impose an A/B pricing structure, as some other processors battling an oversupply, such as Freshways and Yew Tree Dairy, have done.
Medina supplies thousands of hotels, pubs, restaurants and coffee shops both directly and through a range of wholesale customers.
It also supplies 150 hospitals and 110 care homes as well as some 7,000 local convenience stores.
Although, there had been an uplift in retail dairy sales over the past few weeks, the coronavirus lockdown had seen food service sales reduced to almost zero.
Medina chief executive Sheazad Hussain had previously said the company was also working to rapidly take out costs, reconfigure food service operations and looking for ways to address the cashflow issues that the shock to the market and wider economy is causing.