Ramez Azimi, director of the Samaa station in the city of Ghazni, the capital of eastern Ghazni province, said he had received phone calls as well as written warning notes purportedly from the Taliban commander. The commander was not identified.
Azimi said Taliban insurgents, who control several districts in Ghazni province, threatened them because three of the station's 16 employees are women. The Taliban are against women's rights to education and work.
Zabihullah Mujahid, a Taliban spokesman, denied the insurgents had threatened Samaa.
On Saturday, a local radio journalist was killed in neighboring Paktia province. The police said it was not immediately clear if the killing of Nader Shah, a newsreader for Radio Gardez, was linked to his work or a personal dispute.
The developments come despite stepped-up efforts by the United States to find a negotiated end to the country's nearly 18-year-long conflict, America's longest war.
Afghan talks that brought together the country's warring sides ended last week in Qatar's capital, Doha, with a statement that appeared to move closer to peace by laying down the outlines of a roadmap for the country's future.
According to Azimi, the Samaa station was closed four days ago. Azimi told The Associated Press this is its third closure in the past four years. The station was forced to shut down twice in 2015, the first time for a month after which it reopened thanks to mediation by the elders, he said. Later that year it closed again, for nine months.
"At one point, four Taliban fighters came to our home in Ghazni city to threaten me and my brother, who is also working at the station," Azimi added.
Azimi's father, Zarif, a doctor who owns a medical clinic and a pharmacy in the city, says the threats are worrisome.
"I can't stay in Ghazni, I can't let the Taliban harm my sons or any of my family members," he said.