The rating agency also revised the outlooks on the Aaa ratings of the Netherlands and Luxembourg from "stable" to negative." Finland maintained its Aaa rating and stable outlook.
Moody's said the revisions for the three countries were prompted by "the rising uncertainty regarding the outcome of the euro area debt crisis" and the "increasing likelihood that greater collective support for other euro area sovereigns, most notably Spain and Italy, will be required."
The possibility of a Greek exit from the euro, Moody's said, could threaten banks throughout the eurozone. German banks also have significant exposure to other struggling countries on the continent, particularly Italy and Spain, the agency added.
Even if the monetary union remains intact, Moody's said Germany, as the eurozone's largest economy, will likely bear an increased financial burden as further bailout funds are required.
Stocks fell globally on Monday amid fears that Spain may need an expanded bailout package. The yield on 10-year Spanish bonds shot up Monday to a euro-era record of 7.565%, a level widely considered unsustainable.
Fellow ratings agency Standard & Poor's has Germany rated AAA with a stable outlook.