The fast-food chain, which has around 1,300 branches in the UK, has halted the supply of the drinks to branches in England, Scotland and Wales this week.
Brexit immigration rules and coronavirus regulations have caused lorry driver shortages in the country, impacting the supply of food and drink reaching the UK.
McDonald’s said it was, “working hard to return these items to the menu as soon as possible”.
“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,” a spokesperson told the Independent.
“We apologise for any inconvenience, and thank our customers for their continued patience.”
Peri-Peri chicken chain Nando’s had to close 50 of its stores last week as supply chain issues affected its stock of chicken, while fast-food restaurant KFC has also reported problems with its food and packaging supply.
Logistics firms have warned that supply issues in supermarkets could continue for months if labour shortages are not dealt with swiftly. The UK government is facing pressure to allow EU citizens into the UK for Christmas as some companies turn to prison labour to tackle the shortage.