Steinmeier, in Brussels for an EU foreign ministers meeting, said he had met NATO head Jens Stoltenberg earlier Monday "where the statements of President-elect Trump... were received with concern".
"This is in contradiction with what the American defense minister said in his hearing in Washington only some days ago and we have to see what will be the consequences for American policy," added Steinmeier, as reported by AFP.
In interviews with top European newspapers Sunday, Trump rode roughshod over worries in Europe about Washington's near 70-year security guarantee and again displayed his apparent preference to do deals with Russian President Vladimir Putin over their heads.
"I said a long time ago that NATO had problems," Trump told Britain's The Times and Bild, Germany's biggest-selling daily.
"Number one, it was obsolete, because it was designed many, many years ago... Number two, the countries aren't paying what they're supposed to pay."
Spending has been a key source of friction within the 28-nation alliance over recent years, with Washington bearing the brunt of the burden.
Stung into action by Russia's intervention in Ukraine and its annexation of Crimea, NATO leaders have approved its biggest military build-up since the end of the Cold War, but now find themselves facing a president seemingly with other priorities.
Steinmeier said Trump's remarks had caused astonishment and would dominate the foreign ministers meeting.
"This day will be influenced if not determined by the statements of the American President-elect, which caused here in Brussels astonishment and agitation, and I suppose, although I am sure about that, not only in Brussels!"