The town with a population of around 37,000, plus around two dozen villages, clamped the 'bandh' to protest the claim of Parbhani' Pathri village in that the 19th century saint was born there.
All shops and commercial establishments, hotels and restaurants, remained shut on the first day of the bandh.
However, the Saibaba Samadhi Temple functioned as usual, with the poojas and aartis performed as per schedules, the prasadalaya served food add prasad to the pilgrims who thronged there for the weekend darshan, as well as the hospital, hostels, etc, a spokesperson for the Shri Saibaba Sansthan Trust (SSST) Trust, which manages the temple, said.
The shutdown has the support of the local Bharatiya Janata Party MP Sujay Vikhe-Patil and other local organisations.
The protesters have spurned a call by Chief Minister Uddhav Thackeray and other leaders of the ruling Shiv Sena-Nationalist Congress Party-Congress to call off the bandh, and threatened to continue till their demand is met.
The matter snowballed after Thackeray, who last week visited Pathri, termed it the 'birthplace' of Saibaba and announced a Rs 100 crore grant to develop the temple and surrounding areas on the lines of Shirdi, where Saibaba had spent his life of preaching and teaching till he took 'Samadhi' in October 1918.
BJP leader Radhakrishna Vikhe-Patil informed mediapersons that the people of Shirdi have no objections if funds are sanctioned for Pathri's development but had reservations to according it the status of "Saibaba's birthplace".
Taking cognizance of the Shirdi citizens' strong sentiments, Thackeray has convened a meeting in Mumbai on Monday to resolve the sensitive subject.
Meanwhile, hundreds of Shirdi residents took out a procession in the morning and evening carrying banner and placards with photos of Saibaba, raised slogans and staged protests at various locations, sang bhajans and religious songs extolling Saibaba, for their demand.
Similar 'counter-protests' were also held in Pathri with prayers, singing bhajans and religious songs of Saibaba.
The Pathri gatherings demanded that all the available 29 evidences and symbols, official and religious records, proving Saibaba was born here should be submitted to the Shirdi's SSST authorities to resolve the issue amicably.
NCP Minister Chhagan Bhujbal, who prayed at the Shirdi Temple on Sunday, said that the shutdown will not resolve the dispute, calling for negotiations without politicising the issue.
MLC and former MLA from Pathri, Durrani Khan said that there are enough historical evidences available to prove that Saibaba was born in Pathri, and his statement was echoed by NCP Minister Dhananjay Munde.
They urged the people of Shirdi to withdraw their indefinite bandh to avoid inconveniencing the thousands of devotees who visit the town daily.
Union Minister of State Ramdas Athawale said that the protests and shutdown cannot solve the issue and the row must be hammered out with discussions.
( With inputs from IANS )