No, Park Service officials say, Sunset Crater Volcano is not erupting and is considered to be extinct/NPS.

National Park Service officials found themselves having to debunk Internet chatter this week that the main attraction at Sunset Crater Volcano National Monument near Flagstaff, Arizona, has erupted. 

"The Internet source of the purported eruption is based upon a black-and-white satellite image," park staff say. "The report is not from an academic source or part a scientific agency, such as the United States Geological Survey. Furthermore, no activity has been observed on the ground by park rangers staffing the national monument."

Additionally, the Park Service points out, "Sunset Crater Volcano, part of the San Francisco Volcanic Field, is an extinct cinder cone. Local cinder cones are created by a one-time eruption event and are not known to erupt more than once. Sunset Crater Volcano erupted over 900 years ago, making it the youngest cinder cone in a field of over 600 volcanoes. It is now extinct, and not anticipated to erupt again."

At the same time, "According to many geologists, the San Francisco Volcanic Field is still considered to be active, so it's possible that an eruption could occur during the next 1,000 to 5,000 years somewhere east of Flagstaff, Arizona. Come visit Sunset Crater Volcano National Monument to see for yourself and learn more about your park."