Just two months after forming a left-right "grand coalition", Merkel must replace her agriculture minister Hans-Peter Friedrich after he became engulfed in the rapidly widening scandal.
Friedrich, interior minister until December, had come under intense pressure for tipping off the party chief of a prominent MP that the lawmaker was under investigation in the Canadian-led probe.
The leak, which dates back to October, was reportedly aimed at preventing the MP from being included in a new government during negotiations to form a new coalition.
He reiterated earlier remarks that he believed he had "acted politically and legally correctly".
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"But I will also say that the pressure on me has grown so much in the last few hours that the duties ... In the agriculture ministry can no longer be handled with the necessary concentration, calm and political support," he said.
Merkel, still on crutches after a Christmas skiing accident, followed him in front of the TV cameras to announce that she had accepted his resignation "with great respect and great regret".
The case has blown up since news broke early in the week that searches had been carried out at the home and offices of Social Democrat (SPD) lawmaker Sebastian Edathy as part of a child pornography investigation.
German media have linked the probe to a global investigation into a Canadian child porn website.
Edathy - who has gained prominence for heading a parliamentary panel into the shock 2011 discovery of a neo-Nazi killer cell - had stepped down from his Bundestag seat days earlier citing health reasons.
Friedrich faces claims he may have breached secrecy or had an impact on a legal investigation after telling SPD chief Sigmar Gabriel, now Merkel's energy minister and vice chancellor, that Edathy's name was on the investigation list.
The move dates back to October, the month after September 22 German general elections when Merkel's triumphant conservatives were in the process of building a coalition government with the centre-left Social Democrats.