The institute also warned of a volcanic tidal wave and rapid currents of warm gas and volcanic materials that may affect areas around Lake Thal, a popular holiday destination for Manila residents.
The Philippine Institute of Volcanology and Seismology has raised the alert level to a fourth of five, meaning potential volcanic eruptions within hours or days.
The Philippine National Disaster Council said that about eight thousand people were being evacuated from the volcano island and towns at risk, and about six thousand people had already left the dangerous area.
The ashes arrived in Manila, which led to the suspension of flights at the busy international airport.
The local authorities suspended the studies in some schools and urged residents to stay in their homes.
A spokesman for President Rodrigo Duterte said in a statement that the president directed the authorities to move people from the vicinity of Lake Tale out of the danger zone.
Tale Volcano, one of the most active volcanoes in the Philippines, is located in a lake about 70 km south of downtown Manila.