Mansour had been arrested at Tegel airport on an arrest warrant issued by the Egyptian government over his alleged participation in the torture of a lawyer in 2011.
The German Foreign Ministry had said earlier on Monday that it would not extradite anyone to a country where they could face the death penalty, after the government was widely criticized for arresting Mansour.
"I don't think one can say this loudly enough: Of course, nobody will be extradited from Germany who risks being sentenced to death abroad," Foreign Ministry spokesman Martin Schäfer told journalists, including Reuters, in Berlin.
Members of the German opposition had earlier accused the Berlin justice system of complicity in the actions of a 'despotic regime.'
Fraziska Brantner, MP for the Green Party accused the Berlin prosecutor of becoming "an assistant to the despotic regime in Cairo". Her party colleague and party leader Cem Özdemir said that "many question marks" remained over the arrest of Mansour.
The deputy parliamentary leader of die Linke (the Left Party) protested to the Cologne Stadt-Anzeiger newspaper on Monday that "everyone knows that the rule of law in Egypt is a hollow shell, that is if we can even speak of rule of law there".
In a statement on its website, Al-Jazeera said the charges against Mansour brought by the Egyptian government were false.
According to Al-Jazeera, an Egyptian court had sentenced Mansour in absentia last year to 15 years in prison for "torturing a lawyer in 2011 on Tahrir Square" in Cairo.
The arrest warrant against Mansour is a "spurious attempt at character assassination of a leading journalist," the Al-Jazeeera statement read.