The deadly clashes last week marked a rare outbreak of violence between Kurdish forces and Syrian army forces in Qamishli, where control is split between Kurdish militia and the Syrian army and its allies.
The two sides agreed an indefinite ceasefire on Friday but tensions have remained.
"An agreement was reached after midnight to bring calm back to Qamishli involving an exchange of prisoners between both sides," a Kurdish security source told AFP on Sunday.
A government security source confirmed a deal was struck during a meeting at the mainly Kurdish city's airport between government officials and representatives of the Kurdish People's Protection Units (YPG).
"It was agreed to keep Friday's truce in place" with "the exchange of those captured and injured starting Sunday," the government source said.
The fighting began on Wednesday with a scuffle at a checkpoint and, according to Kurdish security forces, killed 17 civilians, 10 Kurdish fighters and 31 government troops and allied forces.
The deal reached on Sunday, according to a Kurdish source, would also see the government free Kurds held in its prisons since before 2011.
Kurds will keep the positions they seized during the clashes, including a prison, the source said.
The sources could not say how many prisoners would be involved in the swap.
Both sides said they would keep channels of communication open to come to an agreement on additional points, including a potential reduced presence for Syrian army forces in Qamishli.
The army and its ally, the National Defence Forces, control Qamishli airport and parts of the city, as well as parts of the provincial capital Hasakeh to the south.
Nearly all of the rest of the province is controlled by the YPG, who have declared an autonomous region across the mainly Kurdish northern areas they control.