Aleppo Residents left Ashrafieh and Sheikh Maqsud during a pause in fighting, carrying belongings and searching for safer areas.
The clashes, which began on Tuesday, are the most serious in months between government forces and the Kurdish-led Syrian Democratic Forces.
At least nine people were reported killed, including civilians, with both sides trading blame for shelling of residential areas.
The violence comes as talks stall over a March agreement to merge Kurdish forces into the national army. Despite meetings in Damascus, officials admit little progress, leaving civilians caught between rival forces in a city already marked by years of war.
