The duo, currently on a European tour, had been expected to play five dates in Britain.
"With late notice of Snoop being denied a visa, time has ran out and it is too late reconfigure the show," the statement said.
Tour organizers had said that the concerts, starting with one at London's Wembley Arena on Wednesday, would go ahead without Snoop Dogg.
British Home Office rules state that foreign citizens can be barred from entering the country if there were concerns about their presence.
In April 2006, Snoop Dogg, whose real name is Calvin Broadus, and five other men were arrested on charges of violent disorder and starting a brawl, and spent the night in jail after trouble flared when some in his party were denied entry to British Airways' first class lounge at Heathrow Airport.
Seven officers received minor injuries — mainly cuts and bruises — and one suffered a fracture to the hand.
Snoop Dogg was previously barred from entering Britain in May 2006.