"The new Greek government has strong public support," Schäuble said in an interview with German newspaper Bild am Sonntag.
"I am confident that it will put in place the necessary measures, set up a more efficient tax system and in the end honour its commitments.
"You have to give a little bit of time to a newly elected government," he told the Sunday paper. "To govern is to face reality."
Schäuble also insisted that his Greek counterpart Yanis Varoufakis, despite their policy differences, had "behaved most properly with me" and had "the right to as much respect as everyone else".
It was a marked change in tone for the strait-laced Schäuble, who has repeatedly exchanged barbs with Varoufakis, his virtual opposite in both style and politics, since January's watershed Greek elections brought in an anti-austerity government.
Schäuble last week sternly warned that Greece would not receive "a single euro" until it meets the pledges of its existing €240 billion ($270 billion) bailout programme.
But he put his weight behind a four-month extension, to the end of June, approved overwhelmingly by the German parliament on Friday after a complex compromise reached between eurozone finance ministers and Athens.
In exchange, Greece has pledged to implement reforms and savings.
Schäuble reiterated the ground rules for the aid programme extension, stressing that "Greece must meet its commitments. Only then will it receive the promised aid payments."
Asked about repeated comments from the new Greek government against austerity measures and for a debt haircut, Schaeuble said that "contracts are more important than statements".