The blast was caused by a truck bomb which struck near a Kurdish security headquarters, according to a UK-based monitoring group.
So-called Islamic State (IS) has said it was behind the attack, in Hassakeh province, near the border with Turkey.
IS has previously carried out bombings against Kurds in the area.
A Kurdish-dominated militia backed by air strikes from the US-led coalition is spearheading the battle against IS in northern Syria.
State TV showed scenes which it said were the aftermath of the bombing, with pictures of destruction over a large area and plumes of smoke rising into the air.
An eyewitness told the BBC that there are people trapped under the rubble and there are fears the death toll may rise. More than 100 people have been wounded.
IS said on its self-styled Amaq news agency that a suicide bomber had blown up a truck at a local Kurdish police centre and a nearby government building.
The attack was initially reported as a double bombing, but it now appears that the first blast caused a gas tank to explode, according to AFP.
Hospitals in the city are calling for blood donations, the Syrian Observatory for Human Rights monitoring group reports.
The dead include civilians and members of the security forces, it says.
While Qamishli has been targeted before, the group says this is the biggest explosion ever to hit the city.
The blast shattered windows in the Turkish town of Nusaybin, across the border, Reuters reports. -BBC