Lambrecht asked the chancellor to dismiss her, as formally required, and Scholz has accepted it, a government spokesperson said.
The chancellor would propose a successor promptly, the person added, refusing to comment on names.
Parliamentary Commissioner for the Armed Forces Eva Hoegl, junior defence minister Siemtje Moeller, SPD party head Lars Klingbeil and Labour Minister Hubertus Heil have been suggested as candidates by German media.
The Frankfurter Allgemeine Zeitung newspaper said, citing government sources, that a successor would be announced on Tuesday.
Marie-Agnes Strack-Zimmermann, the head of Germany's parliamentary defence committee and a member of Scholz's junior coalition partner Free Democrats (FDP), called for her successor to be installed quickly.