The German government overwhelmingly approved the deal after Finance Minister Wolfgang Schauble warned "a Greek bankruptcy could lead to the break-up of the eurozone."
The vote was 473 approving, 100 voting no and 11 abstentions, the BBC reported.
The vote followed an agreement among finance leaders of the 17 eurozone nations Monday to go ahead with payments to Greece that had been delayed since June.
But the bailout effort also hit a new hurdle when the International Monetary Fund said it would not give its part of the money until Greece buys its bonds back.
IMF Managing Director Christine Lagarde "would be in a position to recommend to our executive board the completion of the first review of Greece's program" only after Athens delivers "on the commitments agreed, in particular the implementation of debt buybacks," IMF spokesman Gerry Rice told reporters.
The IMF, based in Washington, is responsible for about 20 percent of the $319 billion in bailout money promised to Athens to date.
The buyback is supposed to cut Greece's debt burden by 10 percent of gross domestic product, deemed crucial for restoring the country's long-term financial viability, the British newspaper The Daily Telegraph said.
If the IMF withdraws, Finland and Holland will also pull out of the program, the newspaper said.
"This has become a really big problem," Raoul Ruparel, head of economic research at London's Open Europe think tank, told the newspaper.
Open Europe, which has offices in Berlin and Brussels, promotes EU economic and political reform.
Rice said the IMF would give Athens until Dec. 13 to buy back the bonds.
That is when Jean-Claude Juncker, president of the eurogroup of finance ministers, said the ministers expected to release their share of about $44.7 billion of Greece's $57.9 billion bailout installment -- delayed multiple times since June.
The dispute comes as Moody's Investors Service said the EU-IMF deal worked out Tuesday to unlock the bailout installment merely papers over cracks and doesn't change Greece's "extreme economic and social fragility."
"We believe that the country's debt burden remains unsustainable," it said.
Moody's said EU countries and official creditors must agree to write down their holdings or there would be no lasting solution to Greece's debt crisis.
Private investors, mostly financial institutions, are furious at demands they take a second "haircut" of 70 percent on their remaining holdings after already taking a 53.5 percent loss earlier this year while official creditors refuse all losses, the Telegraph said.