"It's important that Spain use the financial instruments to recapitalise its banks," Weidmann told public television station ARD in an interview.
"I am confident in the Spanish government, which has already begun undertaking full measures in the labour market. But that path must continue."
The Bundesbank president also called for tighter supervision of European banks.
"I consider it wrong to introduce common guarantees as long as there is no credible supervision," said Weidmann, who is also a member of the European Central Bank's governing council.
He also had stern words for Greece, which returns to the polls on June 17 for an election that could determine its future in the eurozone.
"It's up to the Greeks to decide if they want to stay in the euro or not," Weidmann said.
"But it must be clear that the financial assistance that has been granted cannot continue if the obligations aren't fulfilled, because otherwise all the other programmes and commitments linked to them will also be called into question."
He called on the Greek government, to "send a clear signal to show that it is ready to put in motion the reforms it has promised."