A security guard stationed at Bhujbal's official residence in Malabar Hill received a telephone call from the unidentified person who said, "Don't dare step into Nashik," they said.
Bhujbal represents Yeola Assembly constituency in Nasik district.
Immediately after receiving the call, Bhujbal lodged the complaint with the Malbar Hill police on Wednesday, they said.
The phone number of the call has been traced and efforts are on to nab the caller, they said.