"This is a historical moment for the Kurdish people," Merab Shamoyev, chairman of the International Union of Kurdish Public Associations, said at the ceremony in an industrial neighbourhood in southeast Moscow.
"Russia is a great power and an important actor in the Middle East. It is in fact not only an actor, but it also writes the script."
The opening of the representation -- which Shamoyev said was a "big political step" for Syrian Kurds -- came as global powers meet in Munich tomorrow in a bid to revive Syria peace talks.
Those present at the ceremony have ties to the Kurdish Democratic Union Party (PYD), said Shamoyev.
The PYD is a leader in the fight against the Islamic State group in northern Syria, but Turkey considers it to be an offshoot of its arch-foe the Kurdistan Workers' Party (PKK).
The PYD was not invited to the Syria peace talks which collapsed in Geneva last week amid accusations from the West and the Syrian opposition that Russia's bombing campaign was targeting civilians.
Moscow, a long-time supporter of Syrian President Bashar al-Assad, has said no negotiations could yield results without the Kurds but Ankara considers their presence unacceptable, given their desire for independence.
Russia's foreign ministry has appeared to distance itself from the opening of the Syrian Kurdish office, saying Kurdish interests will be represented by diplomats from Syria and Iraq.
Shamoyev expressed hope that the rights of the Kurdish people to have their own "culture, language and self-governance" would be guaranteed by Syria's constitution and that Russia would help them with that.