The British-based Syrian Observatory for Human Rights said at least one of the explosions hit near a security headquarters of the Kurdish administration that controls most of Hasaka province, where Qamishli is located.
State TV said one blast was from a car bomb and the other from a bomb on a motorbike. It said the death toll had reached at least 12 people.
One explosion was so powerful it shattered windows of shops in the Turkish town of Nusaybin directly across the border. Two people were slightly hurt in Nusaybin, a witness said.
Islamic State claimed responsibility for the blasts. The jihadist group, which is fighting against the Kurdish YPG militia and its allies in Hasaka and Aleppo provinces, has targeted Qamishli and the provincial capital, Hasaka city, in the past with bombing attacks.
A suicide blast killed six members of the Kurdish internal security force, known as the Asayish, in April. In July, an Islamic State suicide bomb killed at least 16 people in Hasaka.
The YPG captured large areas of territory from Islamic State in northeastern Syria last year and is involved in a U.S.-backed offensive that has advanced against the jihadists further west near the Turkish border.