The blast that took place near an area where the US embassy and Nato peacekeeping force headquarters are based, injured a security guard inside the TV station. But police could not say if there were any casualties.
The massive blast from the "very strong" rocket sent shrapnel flying hundreds of metres (yards).
Station officials were not immediately available for comment.
Soldiers from the Nato-led International Security Assistance Force (ISAF) have sealed off the area, the source said.
The television station is across the street from the heavily-fortified ISAF headquarters in the barbed wire and blockade-strewn heart of Kabul. The US embassy, other diplomatic missions and UN offices are also located nearby.
There are regular rocket attacks in the city, but they seldom cause much damage or hit any significant targets.
Tight security also spares the capital much of the violence caused by an ongoing insurgency blamed on militants loyal to the fundamentalist Taliban regime that was ousted in a US-led campaign in late 2001.
However two ISAF soldiers, one German and one Portuguese, were killed by suicide attacks in Kabul in November.