Modi was supposed to hold two rallies in the constituency on Wednesday but permission for one of the rallies is yet to be given, the party said.
In Varanasi, ADM (city) MP Singh told PTI that they received the application seeking permission for the rally on Tuesday and the decision will be taken by 5 pm.
BJP media in-charge of Kashi region, Sanjay Bhardwaj said they had sought permission for Modi's rally at Beniabagh ground and another at Jagatpur ground in Rohania.
He said the district administration is yet to give permission for Beniabagh ground rally.
Flaying the district administration, BJP leader Arun Jaitley said, "I don't know who is interfering but the returning officer of this constituency is a threat to free and fair election".
"This is unprecedented and unheard of and the party will not take it lying down," he said when asked if the party would approach the Election Commission over it.
BJP spokesperson Nirmala Sitharaman said the Varanasi administration was obeying an "unwritten order" and there is an "undeclared understanding" between them and the ruling Samajwadi Party.
She said it was for the first time a candidate was denied permission to hold a rally in his own constituency.
Modi is fighting election from the holy city which goes to the polls in the last phase of polls on May 12.
"There is an undeclared understanding between SP and district administration. How can the administration deny permission to a candidate to do it (rally) in his own constituency. It is obeying an unwritten order," she told reporters.
She said though the venue was pre-booked, the payment has not been made yet, suggesting that it was just a pretext to deny permission for rally.
"It is absolutely unacceptable. We are quite surprised," she said.
Image: Narendra Modi flashing victory sign while on his way to file nominations in Varanasi
Photograph: Sandeep Pal