Transportation Ministry spokesman Bambang Ervan said his office has issued a notice Monday for all airlines to avoid routes near the mountain.
Residents in Medan, the provincial capital about 50 kilometers (30 miles) northeastward, could see black smokes billowing from Sinabung.
Hours earlier, Mount Merapi, Indonesia most volatile volcano in Central Java, spewed volcanic ash about 2,000 meters (6,500 feet) into the sky, causing ash to fall in several towns.
National Disaster Management spokesman Sutopo Purwo Nugroho said about 600 families have gathered for a possible evacuation.
Merapi, which is in Yogyakarta province, killed more than 300 people and caused the evacuation of 20,000 villagers when it burst back to life in late 2010.
Indonesia which is located on the so-called Pacific "Ring of Fire," has 129 active volcanoes, making it prone to seismic upheaval.