Many residents have already left the area as a precaution.
An orange volcano alert, the second highest, has been issued in both countries.
The 3,000 m (10,000 ft) volcano is in Argentina’s south-western Neuquen province, which borders the Biobio region of Chile.
Ash has been raining down on the nearby villages of Copahue, Caviahue and Zapala.
Residents who have stayed behind have been told to monitor the situation and be prepared to evacuate.
Planes flying over the southern Andes have also been warned.
Hundreds of flights were cancelled last year due to the eruption of Puyehue volcano, in Chile.
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