The tower was targetted by the unidentified attackers at Gadoodbagh in Habbakadal of downtown Srinagar around noon, sources said.
They said the grenade landed inside the residential compound of Abdul Ahad Haji, which also houses two mobile towers and exploded with a big bang.
The explosion caused damage to a private car parked in the compound, the sources said.
A police spokesman said, "We are investigating the matter and analysing the nature of the explosive."
This is the first such incident in the city after a series of attacks in north Kashmir's Sopore and Pattan townships in Baramulla district and Handwara in Kupwara district which left two persons dead.