Around 20 protesters suffered injuries in clashes with security personnel who used tear gas to disperse the mob protesting the well-known temple in Janakpur, over 225 kms from here.
Tensions were running high when 54-year-old Bhandari arrived on a chopper to offer prayers during the Vivaha Panchami festival, prompting authorities to beef up security in the area.
Hundreds of people took to the streets in Janakpur protesting against her visit as head of the state, and many of them were carrying black flags, according to eye-witnesses.
The injured are undergoing treatment at various local health facilities.
Bhandari's visit was being opposed by the Madhesis - agitating over the new Constitution - as she represents the ruling CPN-UML party.
A petrol bomb was hurled at the temple premises immediately after she left due to which the stage and canopy caught fire, The Kathmandu Post reported.
The President had spent 10 minutes in the temple and protesters pelted stones from all directions, the report said, adding that they even hurled stones at Bhandari's vehicle and some of the vehicles escorting her.
The Madhes-based parties also staged demonstration against the visit of Bhandari - the Vice-president of CPN-UML and widow of late general secretary of the party Madan Bhandari who was elected as Nepal's first woman President by the parliament in October-end.
Madhesis, the Indian-origin inhabitants of the Terai region are agitating over the new Constitution demanding more representation. They are also protesting division of their ancestral homeland under the seven-province structure and have led an ongoing blockade of key border trade points with India.