The fast food giant has also run out of bottled drinks at some 1,250 locations.
A McDonald’s spokesman said staff are “working hard to return these items to the menu as soon as possible”.
He added: “Like most retailers, we are currently experiencing some supply chain issues, impacting the availability of a small number of products. Bottled drinks and milkshakes are temporarily unavailable in restaurants across England, Scotland and Wales.
“We apologise for any inconvenience, and thank our customers for their continued patience.”
It is latest company to be hit by supply issues thought to be caused by a shortage of lorry drivers due to new EU immigration rules brought in after Brexit and Covid restrictions.
Last week, Nandos was forced to close about 50 restaurants because of chicken shortages.
Lobby groups for the retail and transport industries have written to Business Secretary Kwasi Kwarteng with a stark warning about Britain’s lorry driver shortage and the knock on effect to supply chains.
They want a review of plans not to grant temporary work visas to drivers from the EU.
Logistics UK, which represents freight firms, and the British Retail Consortium, said a shortfall of some 90,000 HGV drivers was the root of the problem.
The group said the shortage was “placing increasingly unsustainable pressure on retailers and their supply chains.”
They added: “While there was a shortage of HGV drivers prior to the Covid-19 pandemic and Brexit, these two events have exacerbated the situation.
“The pandemic halted driving training and testing for over 12 months, while an estimated 25,000 EU drivers returned home during the pandemic and following the end of the transition period.”