The two German engineers, who disappeared in northern Iraq on Tuesday, were shown on their knees in front of four kidnappers on the video shown by the television station on Friday.
The tape was dated 24 January, the day they were abducted in the northern industrial city of Beiji, about 240km north of Baghdad.
The hostages, identified by relatives as Thomas Nitzschke and Rene Braeunlich, arrived in Iraq on 22 January.
The German Foreign Ministry said the two only planned to remain in Iraq "for a short time".
They were working for a German company which has a commercial relationship with an Iraqi government-owned detergent company.
In Berlin, Frank-Walter Steinmeier, the German Foreign Minister, said on Friday that contact had been established with the kidnappers.
"The first contact was made by the kidnappers," Steinmeier told RTL television.
He described the pictures as "shocking".
Earlier, Gernot Erler, the Deputy Foreign Minister, told ARD television that a ministry crisis unit "is working constantly to save the two engineers."
American Jill Carroll was seized
by gunmen on 7 January
At least five foreigners have been kidnapped in Iraq this month, including two Kenyan communications engineers missing after an ambush in Baghdad on 18 January.
American journalist Jill Carroll was seized on 7 January in the capital.
Carroll's kidnappers have threatened to kill the 28-year-old freelancer unless all Iraqi women are freed from custody.
On Thursday the US military released five Iraqi women detainees, and a top Iraqi police official, Major General Hussein Kamel, expressed hope the move might help win Carroll's freedom.
No word has yet been heard from Caroll's captors since the detainees' release.
Meanwhile, Iraqi special forces backed by US troops raided houses in Baghdad on Friday and detained at least 35 suspects.
Police said the operation began at about 6 am and was being conducted in several southwestern Baghdad neighbourhoods, with security forces searching homes, stopping cars at checkpoints and frisking people.
It was not immediately clear why the operation was launched, but there has been a large number ambushes and drive-by killings in this sector of Baghdad during the past week.