Jens Spahn said Greece needed “reliability” not debt relief, for its economy to grow – suggesting a reduction or further bailout cash was out of the question.
Greece owes more than £170bn (€200bn) to its creditors, including the EU, the IMF and the European Central Bank.
Its next repayment of £5.9bn (€7bn) is due in July.
But there has been a disagreement between the IMF, which has called for Greece to be given substantial debt relief, and other creditors calling for tougher austerity measures.
Germany, which contributes the most to the Eurozone’s bailout fund the European Stability Mechanism, is among the creditors opposing further handouts.
Mr Spahn, a rising star in German Chancellor Angela Merkel’s cabinet, told radio station Deutschlandfunk: “There must not be a bail-in.
“We think it is very likely that we will come to an agreement with the International Monetary Fund that does not require a haircut.”
He said writing off millions of pounds of Greek debt would upset fellow Eurozone members such as Spain, which has delivered tough reforms.
Finance ministers from the European Commission, the ESM the IMF and the European Central Bank are due back in Athen on Tuesday to continue talks over possible reforms.