AFP journalists who arrived at the scene found fire damage at the entrance to the building and in a washroom, and spray-painted slogans in Hebrew reading, "Siege on Arabs and not on Jews", and "The land of Israel for my people!"
They said the damage was light and the prayer area was unharmed.
The incident bore the hallmarks of a "price tag" attack — a euphemism for Jewish nationalist-motivated hate crimes that generally target Palestinian or Arab property.
"Residents were surprised during the night by a fire in the mosque and rushed to put it out,” Al Bireh Mayor Azzam Ismail told AFP, blaming "Israeli settlers”.
Speaking ahead of a weekly Palestinian Cabinet meeting, Prime Minister Mohammed Shtayyeh called the attack a "racist act” and said he held Israel’s government responsible for "the increasing violence of the settlers”.
Israeli Economics Minister Amir Peretz, of the left-wing Labour Party, called for "the criminals and hatemongers who burned a mosque to be brought to justice”.
"The hate virus, like the coronavirus, is a common enemy of all religions and peoples in the world,” he wrote on Twitter.
"Just as everyone together fights the [corona] virus, we must work together to eradicate the hatred virus as well.”
Some 450,000 Israelis live in West Bank settlements considered illegal by the international community, alongside over 2.8 million Palestinians.