"The People's Protection Units (YPG) fighting the jihadists (IS) for nearly four months have full control of the security district," the Syrian Observatory for Human Rights said.
The Britain-based group said Kurdish fighters had seized control of the area after fierce clashes since Sunday night.
A US-led coalition against IS also carried out at least three air strikes against the jihadist group in the town on the Turkish border, the Observatory said.
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At least 14 IS members were killed in the fighting, it added.
IS began its assault on Kobane in mid-September and came close to overrunning the town, which is also known as Ain al-Arab.
But Kurdish fighters, backed by international air strikes, have been able to gradually recapture territory in the small town, which is strategic because of its location on the border.