"Any other alternative would be much more expensive for the Germans, would be much more dangerous, would carry much bigger risks," Schaeuble said.
He said experts agreed that "it would be disastrous to risk ... a member of the European currency union, Greece, now becoming insolvent".
Germany's government had wanted to wait until after local elections on May 9 to prevent any announcement affecting the outcome of the polls.
The bill will now go to the parliament's upper house and then to Horst Koehler, the president, before becoming law.
The finance is part of a $146bn package to bailout Greece, which is finding it difficult to access money on the open market because of the apparent risks.
Late on Thursday, France's senate approved their nation's contribution to the EU loan package, providing up to $22.5bn over the next three years.
The crisis hurt markets globally on Friday, with bourses in Japan, South Korea, Australia and the UK dropping.
China's benchmark Shanghai index tumbled 2.4 per cent in early trade, though rallied later, with shares in Taiwan, Singapore and New Zealand all falling sharply.
That followed the Dow Jones index's biggest ever intra-day drop causing panic selling in US markets overnight, wiping out billions of dollars in market value.
At the peak of the sell-off, the slump wiped nearly $1trn off the face value of US equities.
The debt crisis in Europe has caused fears that finance for firms in other areas of the world will dry up.
The Bank of Japan said on Friday that it would offer offer two trillion yen ($22bn) in short-term loans to commercial banks to boost liquidity.
Fears of other euro zone nations - particularly those with high debt, such as Spain, Portugal and Italy - being unable to find finance due to the crisis continue.
However, Spain announced on Friday that it had pulled out of recession in the first quarter of 2010, with growth of 0.1 per cent.