"The time for playing games is over," Maas told Deutschlandfunk radio, adding that the EU would deal "constructively" with any British request to delay the departure date.
German economy minister Peter Altmaier said that the EU would look at any fresh proposals London made, but said the substance of the deal was non-negotiable.
But umbrella groups representing German industry, whose cross-border supply chains stand to be hit by the imposition of a hard customs border between Britain and the continent, were less conciliatory.
Martin Wansleben, head of the German Chambers of Commerce, warned that the political uncertainty now made planning almost impossible and that German companies were already starting to build inventory in preparation.
German auto makers would start asking whether it was worth investing in Britain, he added.
"The House of Commons has missed an opportunity to avert a hard Brexit and lay the foundations for close ties to the EU," said Carl Martin Weicker, head of machine tools association VDMA.
"It is simply irresponsible that the British governing coalition is still trying to reach a unified position 10 weeks before the exit deadline," he added. (Reporting by Tassilo Hummel and Arno Schutze, writing by Thomas Escritt; editing by Thomas Seythal and Jason Neely)