The Press Association news agency said members of the star's entourage had hurled bottles of whisky and argued with staff at a duty free shop after being refused entry to a first-class lounge.
London's Metropolitan Police said officers were called to "reports of a disturbance involving 30 people in a business lounge" at Terminal 1 of the busy airport on Wednesday.
When police told the group that they would not be allowed to board their flight, "a number of the group became abusive and pushed officers," a spokeswoman said on the force's customary condition of anonymity.
Six men were arrested on charges of violent disorder and affray and spent the night at London police stations. Police did not name the men, but said all were U.S. citizens in their 30s.
Seven officers received cuts, bruises and other minor injuries, the force said.
Snoop Dogg - real name Calvin Broadus, 34 - had been due to perform in Johannesburg, South Africa, on Thursday.
A former associate of Los Angeles gang the Crips, Snoop Dogg built his early career on recordings offering gritty details of gang life.