Police raided the home of the woman in the coastal city of Port Said and investigators confiscated a laptop, a mobile phone and other equipment she used, the ministry said in a statement.
It said the phone contained video being aired by Al-Jazeera Mubasher Misr just before her arrest. The ministry said the channel stopped broadcasting the video once police had the phone.
A report on Al-Jazeera Mubasher Misr's website identified the woman as Rasha Gaafar and said police arrested her Wednesday. The channel did not say whether she worked for the broadcaster, only that she was charged with filming empty polling stations during the country's presidential election this week.
Egyptian authorities have waged a wide crackdown on the broadcaster since the military's July 3 overthrow of Islamist President Mohammed Morsi. Authorities accused the network of airing biased reports backing Morsi and his Muslim Brotherhood group, designated by the government as a terrorist organization. Al-Jazeera repeatedly has denied the claims.
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The ministry today identified the freelance journalist arrested as a Brotherhood member.
Three Al-Jazeera English journalists arrested in December are on trial on charges of belonging to and aiding a terrorist group, namely the Brotherhood, as well as fabricating footage to undermine Egypt's national security.