One man, Steve Centanni, is an American producer and the other, Olaf Wiig, is a cameraman from New Zealand.
In a news report, Fox confirmed that two employees had been abducted.
It said it did not know who seized them but that "negotiations were under way to secure their release".
There was no immediate claim of responsibility for the abduction.
The witness said two vehicles blocked the journalists' transmission truck in the centre of Gaza City and a masked man put a gun to a bodyguard's head, forcing him to the ground.
The kidnappers then sped away with the two journalists.
A spokesman for Hamas, the resistance group that leads the Palestinian government, condemned the kidnapping.
Khaled Abu Hilal, interior ministry spokesman, said security officials have put police across Gaza on alert and set up roadblocks to find the gunmen and free the reporters.
He said: "This is not acceptable at all."
The New Zealand government has sent diplomats to the region to assist in negotiations.
The head of consular services at New Zealand's foreign ministry, Rosie Patterson, said they were working through the Palestinian Authority.
"We will be putting a team on the ground, so we can have direct liaison with the authority," she said.
Similar incidents in the past in Gaza have ended with the release, usually within hours, of kidnapped foreign journalists or aid workers.