BRUSSELS—Germany’s finance chief questioned a tentative bailout deal for Greece, saying that an exit from the currency union might be a better alternative for the country and its citizens.

Mr. Schäuble’s criticism of the deal now, a day after eurozone leaders agreed to new support for Greece, comes at an inopportune time for Chancellor Angela Merkel, who was central to hammering out the agreement and must now win support for the deal in Germany’s parliament.

Germany—and Finance Minister Wolfgang Schäuble in particular—have driven a hard line on Greece during months of rescue negotiations, even proposing over the weekend that it take a “timeout” from the currency union. But until now, the chancellor and her finance chief have publicly presented a united front.

His comments are likely to bolster critics of the new aid deal—which requires Greece to pass painful austerity measures and relinquish some fiscal controls in return for tens of billions of euros in loans—in Germany’s parliament. Lawmakers in Berlin are slated to vote on the deal, possibly later this week, once Greece’s parliament has passed the first round of measures, including pension cuts and sales-tax increases.

Asked about the idea of a Greek exit from the eurozone, Mr. Schäuble told journalists “there are many people inside the German government…who believe that this would be, or could be the better solution for Greece and the people in Greece.” He didn’t say whether he was one of them, although many European officials say the hawkish German finance chief has done little to hide his support for a currency union without Greece during crisis talks in recent weeks.