They have also seized equipment belonging to the Qatari station's Egypt affiliate, an executive of the Qatari broadcaster told AFP.
Correspondent Wayne Haye, from New Zealand; South African cameraman Adil Bradlow and Irish producer Russ Finn remained in prison after their arrest on Tuesday on unclear charges, the executive said.
They were freelancing for the channel when they were arrested. The detained men do not appear to have had press accreditation at a time when authorities have made it increasingly difficult for visiting journalists to obtain permits.
Egyptian authorities and media have accused Al-Jazeera of biased reporting on the popularly backed coup that toppled Islamist president Mohamed Morsi on July 3 and on its bloody aftermath.
The government has levelled similar accusations against other foreign media.
Police have also detained a correspondent for Al-Jazeera's Arabic channel, Abdullah al-Shami, and Mohamed Badr, a cameraman for its Egyptian affiliate, for more than a month.
A ministry statement said the channel was "operating without any licences."
But the head of the channel, Ayman Gadallah, told AFP yesterday it had received a permit to operate.
State media reported earlier this week that the government called for closing down the channel, which had already relocated much of its operations to Qatar.
