A further three British people and the pilot were injured when the accident happened at around 5:20 pm (0020 GMT) on Saturday.
"We are providing support to the families of six British visitors involved in a helicopter accident at the Grand Canyon on 10 February, and we are in close contact with the US emergency services," a spokeswoman for the foreign ministry said.
Local media reported the Eurocopter EC130 helicopter, whose operator was unknown, was travelling on a tour.
Francis Bradley, Hualapai Nation police chief, said the chopper went down in Grand Canyon West, located in northwestern Arizona.
"The investigation is ongoing," Bradley said on Saturday, adding that there was no information immediately available on the circumstances surrounding the tragedy.
Allen Kenitzer, of the Federal Aviation Authority’s Office of Communications said that the aircraft sustained "substantial damage."
The FAA and the National Transportation Safety Board will investigate the crash, he added. VNS