The Syrian Observatory for Human Rights monitoring group reported several wounded in the attack after midnight in the Tal Saman area in Raqa province, but did not give an exact figure.
There was no immediate Russian report of the incident, which occurred in a broader area controlled by Kurdish-led forces but where the Syrian regime and its ally Russia are also present.
A statement circulated on social media and attributed to the Al-Qaeda-linked Hurras al-Deen jihadist group claimed the attack.
The Observatory said two men parked an explosives-laden pickup truck outside the base and fled, in what was a rare such assault by Hurras al-Deen in the area.
"It's the first such direct attack against a Russian base in northeastern Syria," Observatory chief Rami Abdel Rahman said.
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Hurras al-Deen has fighters in the country's last major rebel bastion in the northwestern region of Idlib, but very rarely operates outside that area.
Russia entered Syria's war in 2015, and its air force has backed Damascus regime forces in several deadly military campaigns against Idlib.
Russia has repeatedly accused rebels in Idlib of attacking its Hmeimim airbase west of the opposition stronghold with drones, but car bomb attacks are much rarer.
Russian troops are stationed in northern Syria, including as part of several deals brokered with rebel backer Turkey.
Syria's war has killed more than 387,000 people and displaced millions from their homes since starting in 2011 with the brutal repression of anti-government protests.
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