Berlin hopes that removal of the bad holdings from balance sheets will encourage banks to lend to each other, to businesses and also consumers.
It is hoped that this in turn will kick-start the economy, Europe's biggest, which is expected to shrink six per cent this year.
Thomas de Maiziere, the chief of staff of Angela Merkel, Germany's chancellor, said: "In the interests of the real economy, we are buying time so that the so-called toxic assets can be cleared up."
With an election looming in September, politicians have been torn between the urgent economic need to revive Germany's troubled banking sector and the political desire not to saddle tax paying voters with a huge bank bailout bill.
Steinbrueck said: "If we do not do something ... if we do not try to solve this problem, then we would have worse problems. We must act."
The finance minister said the plan would "relieve the taxpayer as much as possible."
He said banks would "remain responsible" for their toxic assets, which are mainly comprised of complex financial products based on now worthless "subprime" US property holdings.
After the 20-year period, the value of the toxic assets will be assessed with the banks' shareholders picking up the tab if they have not gained in value.
Steinbrueck estimated that the total value of such assets in Germany was $245bn to $259bn.
Andreas Schmitz, from the federation of German private banks, said the scheme was akin to "a huge deep-freeze in which each bank will have a shelf".
"Their [the bank's] problem assets will be stored there and frozen. After the crisis, we will see if the merchandise can still be sold," he said.
Christoph Schalast, a professor from the school of finance and management in Frankfurt criticised the scheme, describing it as a "bad compromise."
He said: "On the one hand you want to kick-start the credit markets but you want to do it in such a way that the taxpayer pays almost nothing.
"These two objectives seem to me to be difficult to reconcile."
Berlin's plan follows a slightly different model than efforts in other countries to relieve banks of their toxic assets.
In Ireland, the government has set up a single government-backed "bad bank" into which its troubled financial institutions can pour their distressed assets.
Washington has opted to encourage private investors to buy up the troubled assets alongside the taxpayer.
The International Monetary Fund has said that clearing up toxic assets from banks' balance sheet is the top priority for policymakers seeking to drag the global economy from its worst downturn since the Great Depression in the 1930s.