At least one of the blasts in the city of Qamishli was caused by a suicide bomber, the Britain-based Syrian Observatory for Human Rights told AFP.
An AFP correspondent in the city said the suicide attack took place in a restaurant in a Christian neighbourhood.
"Three explosions, one by a suicide bomber inside a restaurant, hit... Qamishli city in Hasakeh province," the Observatory's director Rami Abdel Rahman told AFP.
News agency Amaq, which supports Islamic State militants, said the group had claimed responsibility for the attacks on the city, which lies near the border with Turkey and close to Iraq.
"Dozens of dead and wounded in the bombings by the fighters of the Islamic State in different parts of Qamishli city," it said.
Qamishli is under the shared control of the Syrian regime and Kurdish authorities, who have declared zones of "autonomous administration" across parts of north and northeast Syria.
Syrian troops and seasoned Kurdish fighters have coordinated on security in Hasakeh province where Islamic State militants have tried to advance.
According to the Observatory, all three of the restaurant explosions happened in a zone controlled by regime forces.
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