Shops and other business establishments remained closed while public transport was off roads due to the shutdown, officials said.
Separatists' Joint Resistance Leadership, consisting of both factions of Hurriyat Conference and JKLF, have called the shutdown to demand that Bhat's mortal remains be returned for burial in Kashmir.
The authorities have placed Syed Ali Shah Geelani, Mirwaiz Umar Farooq and several other separatist leaders under house arrest to prevent them from holding protest marches, the officials said.
Adequate security personnel has been deployed at vulnerable places in the Valley, they said.
Movement of people has been restricted in some areas of Srinagar, including Maisuma, the JKLF stronghold, the officials added.
Bhat was hanged and buried inside Tihar jail on February 11, 1984, following his conviction in the killing of an intelligence official.