"There must not be a bail-in," Jens Spahn told German broadcaster Deutschlandfunk, according to a written transcript of the interview.
"We think it is very, very likely that we will come to an agreement with the International Monetary Fund that does not require a haircut," he said, referring to losses that Greece's creditors would have to take if debt was written off.
The IMF has called for Greece to be granted substantial debt relief, but this is opposed by Germany, which makes the largest contribution to the budget of the European Stability Mechanism (ESM), the euro zone's bailout fund.
Greece and its creditors agreed on Monday to further reforms by Athens to ease a logjam in talks with creditors that has held up additional funding for the troubled euro zone country.
Inspectors from the European Commission, the ESM, the IMF and the European Central Bank are due to return to Athens this week.
Spahn, a senior member of Chancellor Angela Merkel's conservatives, said Greece's problem was a lack of growth rather than debt and giving Athens debt relief would upset other euro zone countries such as Spain that had to deliver tough reforms.
"Our Spanish friends, for example, say: 'Hang on - that wouldn't be fair: we carry out reforms and get no haircut and now you're talking about giving Greece one?!'"
Spahn said Germany was campaigning hard to keep the IMF on board in Greece's bailout because of its expertise in helping countries that need to deliver reforms in return for aid.