Three attackers stormed the Shamshad TV building after detonating explosives, police say.
A guard and one of the attackers are said to have been killed and a security operation is under way.
The exact number of casualties is not yet clear. So-called Islamic State said they were behind the attack, in a statement made on its news outlet Amaq.
Shamshad TV quickly went off air after the attack began.
"Some of my colleagues were killed and injured. I managed to escape," Hashmat Istankzai, a reporter for the Pashto-language channel.
Shamshad TV broadcasts a wide variety of programmes including news and current affairs in the Pashto language. It is one of the BBC's partner stations.
Kabul has been targeted repeatedly in recent months by the Taliban and so-called Islamic State militants.
Afghanistan is one of the world's most dangerous countries for journalists and media workers.
In May a BBC driver was among more than 150 people killed in a huge suicide bombing in the capital. Last year seven members of staff from the private Tolo television station were killed in a Taliban suicide bombing in Kabul.
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