The extremist group said in a statement posted online that the attacks in the predominantly Kurdish province of Hassakeh targeted offices of the main Kurdish militia known as the YPG.
The attacks in the town of Tal Tamr occurred late yesterday.
Syrian state media and an activist group said the blasts targeted a medical center and a busy market.
Tal Tamr, once inhabited by Assyrian Christians, is now an overwhelmingly Kurdish town where the main Kurdish fighting force in Syria People's Protection Units, or YPG is in control. The group is the most effective fighting force against the IS.
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Also today, the Observatory and the Local Coordination Committees, another opposition group that tracks the civil war in Syria, reported that warplanes struck small, primitive oil refineries used by villagers in the eastern province of Deir el-Zour. The Observatory said the warplanes were believed to be Russian.
The LCC said seven people were killed and others were wounded while the Observatory said dozens were killed or wounded in the attack on the villages of Zgheer and Kasra.
The Islamic State group today accused Somalia's al-Qaida affiliate of killing several jihadi leaders who defected to its side, including a Sudanese sentenced to death for killing a US diplomat in Khartoum and his driver.
A detailed report posted on two IS-affiliated websites today said al-Shabab leaders ordered the killing and detention of dozens of jihadis who expressed their willingness to join IS. They include Mohamed Makawi, a Sudanese who took part in the drive-by shooting of John Ganville and his driver in Khartoum on Jan 1, 2008.