The four survivors were airlifted to a Nevada hospital while crews were recovering the three bodies, authorities said.
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Six passengers and a pilot were on board the Papillion Grand Canyon Helicopters chopper when it crashed under unknown circumstances about 5:20pm on Saturday (local time) on the Hualapai Nation near Quartermaster Canyon, which is near the Grand Canyon's West Rim.
Hualapai Nation Police Chief Francis Bradley said the survivors were taken to a Las Vegas hospital.
The identities and nationalities of the dead and injured were not immediately released.
"We are in the recovery and investigation mode now," Mr Bradley said.
He said National Transportation Safety Board officials were expected at the crash scene to begin investigating the cause.
The Federal Aviation Administration would also be investigating the crash of the Eurocopter EC130, spokesman Allen Kenitzer said.
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Mr Bradley said rescue crews were hampered by high winds and darkness on Saturday night along with rugged terrain.
"First responders had to be flown in and walk to the crash site," he said.
"Quartermaster Canyon is an extremely remote area.
"We had to call in specially trained crews - people with night-vision goggles."
National Weather Service meteorologists in Flagstaff and Phoenix said wind conditions were an estimated 16 kilometres per hour with gusts of 32 kilometres per hour around the time of the crash.
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Calls and emails to Nevada-based Papillion for comment on the crash were not immediately returned on Sunday.
The company's website said it flies roughly 600,000 passengers a year around the Grand Canyon and on other tours.
It also notes that it "abides by flight safety rules and regulations that substantially exceed the regulations required by the Federal Aviation Administration".
In August 2001, a Grand Canyon tour helicopter operated by Papillon crashed and burned near Meaview, Arizona. The pilot and five passengers died.
An NTSB report issued in 2004 blamed the pilot's decision to descend too fast and too close to the scenic Grand Wash Cliffs.