The Bradford-based grocer's chief executive, David Potts, said: "The bottom line is there are not enough HGV drivers in the country, which is why I believe that skilled work should be added to the shortage occupation list by the Government for a period.
"The whole point about society is to be adaptable and adapt to a crisis."
Asked whether he is calling on the Government to let Eastern European drivers back into the UK, he said: "Yes. They should have done this earlier than now and we need as many as are required to get the country through a dearth of drivers."
In a bid to solve the looming crisis, Morrisons has advertised internally to ask colleagues if they want to train to become HGV drivers.
"We've had 1,651 applicants. We said: 'Does anyone fancy driving a big lorry?' " said Mr Potts.
"Obviously one has to vet them. They're not going to let me loose in an HGV."
Morrisons currently has 400 vacancies for drivers.
The firm also warned of the pressure on prices due to the lorry driver shortage. Mr Potts said the group has seen price inflation start to come through over the past month. This has hit the price of beef and wheat-based items.
Mr Potts said: "Yes of course there is a lot of pressure on beef, but equally pork prices are coming down so as we look ahead to Christmas and Halloween, those items that are inbound from Asia currently on the water, those freight containers are costing 10 times what they were last year.
"It's just a fact. Halloween uniforms, Halloween stuff that you put in your house to scare people and all of the Christmas paraphernalia are all coming over in containers that are 10 times the price of last year.
"Those items that are coming over will, I think, cost a bit more."
He said containers that cost £1,100 each last year now cost £11,000.
"However, the big part of Halloween will be pumpkins and the big part of Christmas is the centerpiece of which we are 100 per cent British around pork, beef, lamb and poultry," he added.
"Price moves are really the last resort in a relatively inflationary environment."