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.
The Kremlin said all five people on board were assumed dead.
"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.
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.
The Syrian Observatory for Human Rights, a Britain-based monitor, said the helicopter had come down along the administrative border between Idlib province in the northwest and neighbouring Aleppo.
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.
Aleppo rebel assault
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 Sunday to try to ease a government siege of the rebel-held east of the city.
The Observatory 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.
The primary goal of the rebel assault is to seize the Ramussa neighbourhood on the southern outskirts of Aleppo.
"The road that runs through Ramussa is the main supply route for regime forces going to the areas they control in western Aleppo," said Observatory head Rami Abdel Rahman.
It is also used by civilians to move in and out of government-controlled districts of Aleppo. Taking a detour from the north of the city would be too dangerous, he added.
Islamist group Ahrar al-Sham said on Twitter it was involved in fierce clashes near Ramussa and advancing towards the route.
State news agency SANA said rebel rocket and sniper fire near Ramussa on Monday killed four people, including three women.
The Observatory put the toll at six dead, including three women and a child.
'Humanitarian corridors'
SANA said people were using the route as usual, but residents of western Aleppo expressed fears that the assault could cut them off.
"If the militants break the siege, they will besiege us and cut the Khanasser route, which is the only artery we have," said Hossam Qassab, a 32-year-old pharmacist.
A Syrian security source acknowledged the assault but said it had been repelled by government forces.
The encirclement of eastern Aleppo has raised fears of starvation for remaining residents, who have reported food shortages and spiralling prices since the government siege began on July 17.
Last week, Moscow announced the opening of "humanitarian corridors" from the east into government territory for civilians and surrendering rebels wishing to leave.
On Saturday, Moscow and Syrian official media reported dozens of civilians had fled via these corridors, but residents and rebels on the ground dismissed the reports as "lies".
Elsewhere in Aleppo province, the Syrian Democratic Forces, a US-backed Kurdish-Arab alliance, advanced inside the Islamic State group bastion of Manbij on Monday, the Observatory reported.
The SDF hold approximately 40 percent of the town, and are fighting to take it with support from the US-led coalition against IS.
