Also in the advert are Somali runner Mo Farah, Jamaican-born footballer Raheem Sterling, Irishman Eoin Morgan and Samoan-born rugby player Manu Tuilagi. All four now play sport in the UK.
Members of the public took to Twitter to vent their fury at the “insensitive” ad.
@IanmAllan wrote: “Does this mean all Scots living in England are immigrants? I came here by car and not in the back of a lorry!”
Others appeared to show sympathy for those attempting to cross the channel into the UK.
One wrote: “What an odious band of f***wits @paddypower are. They should take a look at Calais before making jokes like this.”
However Paddy Power has insisted the advert, which was spotted on the side of a lorry at the port of Dover, is “just a joke” and pokes fun at Murray’s love for Scotland.
Paddy Power causes outrage with Andy Murray ‘immigrant’ advert