The Israeli newspaper reported Palestinian sources said the settlers torched the mosque in the village of Qusra, south of Nablus, about 3 a.m. Monday.
The fire came hours after the destruction of the three houses by Israeli police officers, Haaretz said.
The burning of the mosque brought criticism from the Palestinian Authority, which said settlers have burned other mosques in the West Bank and urged the Middle East Quartet to take action.
Haaretz said about 200 settlers had tried to block bulldozers so they couldn't destroy the structures, leading to the arrest of six youths.
As police officers started emptying the buildings, Regavim, a settlers' advocacy group, sought an Israeli Supreme Court injunction to stop the demolition and won a delay. But the court later issued another order sanctioning the demolition and overriding the injunction.
The Supreme Court had ordered the three buildings be destroyed this year.
"The decision to demolish the houses was made by the government, not the court. Thus the responsibility for this futile action lay with the government. It is still not too late for the prime minister to reverse the decision," said Danny Dayan, chairman of the Yesha Council of West Bank settlements.