The arrest comes two days after American and Iraqi forces detained a freelance photographer for the Reuters news agency south of Baghdad.
The cameraman, Omar Husham, 28, was arrested at his house in the predominantly Sunni neighborhood of Azamiyah, said the television official, who spoke on condition of anonymity because of security reasons. His father and two brothers were also detained, the official said.
The U.S. military said it was looking into the report and did not have immediate comment.
The official said Husham had been working for Baghdad TV for two years and covered many political events.
Baghdad TV is owned by the Iraqi Islamic Party, the major Sunni political group and a member of the Shiite-led Iraqi government.
"Husham is a respected cameraman who has traveled abroad with government officials," the official told The Associated Press. "We demand that concerned officials intervene and for the Americans to release him immediately."
Azamiyah had been a center for Sunni insurgent operations until the U.S. military walled off the center of the district and organized a group of local Sunni fighters who had turned against the insurgents.
Even with the neighborhood's concrete walls, a suicide bomber last month killed Farooq al-Obeidi, the deputy head of the U.S.-allied Sunni fighters in Azamiyah. Nine other people were killed.
Since the U.S.-led invasion of 2003, the U.S. military has detained a number of Iraqi journalists working for international news organizations, including The Associated Press. None has been convicted in an Iraqi court.
On Tuesday, U.S. and Iraqi forces arrested Reuters freelance photographer Ibrahim Jassam during a raid on his home in Mahmoudiya, about 20 miles south of Baghdad, the London-based news agency said. Reuters has demanded that the U.S. either charge or release him.
The U.S. military said Jassam was detained because he was "assessed to be a threat" to Iraq and coalition forces but did not give more details.
In April, the U.S. military freed Bilal Hussein, an AP photographer who was among the recipients of a 2005 Pulitzer Prize for spot news photography from Iraq. He had been held for just over two years.