The attack came as Syrian opposition fighters and their jihadist allies battled government forces outside Aleppo in a bid to ease the regime's siege of rebel-held parts of the northern city.
Russia's defence ministry announced the downing of the helicopter, which it said was carrying three crew and two officers.
"A Russian Mi-8 military transport helicopter was shot down from the ground after delivering humanitarian aid to Aleppo," the defence ministry said in a statement quoted by Russian news agencies.
"As far as we know from the information we've had from the defence ministry, those in the helicopter died, they died heroically, because they were trying to move the aircraft away to minimise victims on the ground," Kremlin spokesman Dmitry Peskov told journalists.
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It was not immediately clear who was responsible.
The incident was the deadliest single attack on Russian forces in Syria since Moscow began its intervention in support of President Bashar al-Assad's government last September.
It brought the total number of members of the Russian forces killed in Syria to 18.
Idlib is held almost entirely by a powerful coalition of Islamist and jihadist forces including the former Al-Nusra Front, now known as the Fateh al-Sham Front after renouncing its status as Al-Qaeda's Syrian affiliate.
In neighbouring Aleppo province, the Fateh al-Sham Front and allied Islamist rebel groups were fighting fierce battles on Monday against regime troops on the outskirts of Aleppo city.
The clashes are part of an assault launched yesterday to try to ease a government siege of the rebel-held east of the city.
It said the rebels had advanced overnight south and southwest of Aleppo but reported ongoing fighting, as well as government air strikes on the battlefield and rebel-held eastern neighbourhoods.
Once Syria's economic powerhouse, Aleppo city has been roughly divided between government control in the west and rebel control in the east since mid-2012.
In recent weeks, government forces have encircled the east, cutting the sole supply route in and raising fears of a humanitarian crisis for the estimated 250,000 people now under siege there.