The Israeli army and police opened a joint investigation into the incident, described as serious by officials.
Residents in the village of Maghayer near Ramallah and the illegal Israeli Alei Ayin outpost dismantled by Israeli security forces last week found fuel soaked tires that had been set on fire and rolled towards the mosque, Ynetnews.com said.
A rug inside the mosque was set afire, Haaretz said. The Palestinian news agency Ma'an said the mosque was almost totally destroyed and its contents incinerated.
Hebrew slogans "price tag," and "Alei Ayin" were sprayed on the walls, Ynetnews.com said.
Palestinian Authority President Mahmoud Abbas issued orders to immediately refurbish the building, the Palestinian news agency said.
The National Christian Coalition in the Holy Land condemned the incident, the third such in the West Bank in the past three years, the agency said.