Ahmed Mansour, who works for the channel's Arabic-language service, was detained as he tried to board a flight from Berlin to Qatar.
A German police official said Egyptian authorities had issued an international arrest warrant for Mr Mansour.
A court in Egypt's capital Cairo sentenced him to 15 years in prison in absentia last year on torture charges.
Al-Jazeera says the claims made against Mr Mansour, who has dual British and Egyptian citizenship, are absurd and false.
"I am still under arrest at Berlin airport, waiting to be taken before an investigating judge," Mr Mansour, 52, tweeted on Saturday night.
Al-Jazeera reports that he is expected to remain in custody until Monday when he will go in front of a German judge.
A police spokesman said the arrest was made at 15:20 local time (13:20 GMT).
He added that the Egyptian-issued arrest warrant accused Mr Mansour of committing "several crimes" but he gave no further details.
Al-Jazeera said the Egyptian warrant was previously rejected by international police body Interpol as it did not meet its rules.
In a video recorded while detained, Mr Mansour described the incident as a "misunderstanding" and said he hoped it would be resolved quickly.
"It is quite ludicrous that a country like Germany would enforce and support such a request made by a dictatorial regime like the one we have in Egypt," he added.
"Other countries must not allow themselves to be tools of this media oppression, least of all those that respect freedom of the media as does Germany," said al-Jazeera acting director General Mostefa Souag.
Relations between Doha and Cairo have been strained by Qatar's support for the now-banned Muslim Brotherhood organisation in Egypt.
Three al-Jazeera journalists, including Australian Peter Greste, were arrested in Egypt in 2013 on charges of supporting the Muslim Brotherhood.
Mr Greste was deported to Australia after being held for over a year.
The other two - Canadian Mohamed Fahmy and Egyptian Baher Mohamed - were released on bail in February pending a retrial.
Egyptian President Abdul Fattah al-Sisi visited Germany earlier this month and met with Chancellor Angela Merkel.
Al-Jazeera says one of its senior journalists has been arrested in Germany at the request of Egypt.