Isaf gave no details on the nationalities of the casualties, but Russian news agencies reported that the aircraft was an MI-8 helicopter belonging to Russian company Vertikal-1.
"A Mi-8 transport helicopter crashed at take-off from an airfield in Kandahar, Afghanistan," a spokesman for Russia's Federal Air Transportation Agency told the Interfax news agency on Sunday.
Interfax reported that the helicopter was carrying three crew members and 17 passengers.
Also on Sunday, a suicide bomber in Torkham, a key border crossing between Afghanistan and Pakistan in Nangarhar province, killed two policemen and a civilian, the Afghan interior ministry said.
In a separate attack, Jan Mohammad, a provincial election candidate, was killed by armed men as he campaigned in northern Kunduz province.
Mohammad is the third provincial election candidate to be killed since registration for the polls in May.
Afghanistan has been hit by a surge of violence weeks ahead of the country's presidential and provincial council elections on August 20.