UK citizens will retain their residence rights for a three-month-period with further extensions possible.
The spokesman added that during that time, they would have to register to acquire a formal right to remain.
A transport ministry spokeswoman said Germany was in close contact with Britain with a view to avoiding disruption to air transport links in the case of a disordered Brexit.
It comes as Mrs May is set to intensify efforts to win over her Brexit critics and seek fresh guarantees from Brussels ahead of next week’s crunch vote on her deal, expected on January 15.
The PM has acknowledged that she was “still working on” getting further assurances from the European Union to address concerns about the backstop measure aimed at preventing a hard border with Ireland.
Meanwhile a major exercise was carried out in Kent involving dozens of lorries.
The trial aimed to test out Manston airfield near Ramsgate as a mass HGV holding bay to ease congestion on roads to Channel ports.
Additional reporting by Reuters.
