Rösler told ARD public television that Athens' partners would wait for the progress report of the troika of Greek creditors - the European Union, International Monetary Fund and the European Central Bank.
"Nevertheless I have to say I am more than sceptical," said Rösler, who is also head of the pro-business Free Democrats (FDP), junior partners in Merkel's centre-right coalition government.
"Unfortunately it is likely that Greece will not be able to fulfil (the troika's) requirements. And I say quite clearly, if Greece fails to comply with the requirements that there should be no more payments to Greece."
He said that an end to further international support might prompt the Greeks to conclude "that it is perhaps smarter to leave the eurozone."
"I think for many experts, for the FDP, for me, that an exit by Greece from the eurozone lost its horror a long time ago."
Troika auditors are expected in Athens this week for a close inspection of the economic programme rolled out by the country's new government.
Their report will determine whether Greece will receive fresh loans of €31.5 billion ($38.3 billion) by September due under its debt rescue programme.
Rösler and his party have frequently expressed doubts about whether Greece is prepared to follow through with the painful reforms necessary to stay in the single currency club.
The FDP is struggling in voter polls to stay above the five percent required for representation in parliament ahead of next year's general election.