Among the Syriza rebels was former Finance Minister Yanis Varoufakis, who was sacked by Tsipras last week and who denounced the bailout deal as "a new Versailles Treaty" - the agreement that demanded unaffordable reparations from Germany after its defeat in World War One.
Energy Minister Panagiotis Lafazanis and Deputy Labour Minister Dimitris Stratoulis also voted against the package.
Amid speculation that both ministers could lose their jobs in a reshuffle, possibly as early as Thursday, Lafazanis said he remained loyal to the government but was ready to offer his resignation, joining Deputy Finance Minister Nadia Valavani, who stepped down earlier on Wednesday.
"We support Syriza in government and we support the Prime Minister. We don't support the bailout," he said after the vote.
Elected in January on an anti-austerity platform, Tsipras made an about-turn following gruelling all-night negotiations in Brussels on Monday, giving in to lenders' demands for immediate reforms to prevent a chaotic exit from the single currency.
Speaking in parliament before the vote, Tsipras made clear he was supporting the package against his will but there was no alternative if Greece was to avoid financial collapse.
"I acknowledge the fiscal measures are harsh, that they won't benefit the Greek economy, but I'm forced to accept them," he said as he made a final appeal for support.