Standard & Poor's has warned that current proposals for restructuring Greece's debt would effectively constitute a default.
The ratings agency said plans for the private sector to roll over debts could trigger a default under its ratings criteria.
Last week, the Greek parliament passed tough austerity measures to secure further financial aid.
However, there is a growing sense that a debt restructuring is inevitable.
German and French banks have already agreed in principle to roll over loans to Greece in order to give the country more time to repay its debts.
This could involve effectively reinvesting the proceeds of maturing Greek debt into newly-issued bonds.
Standard & Poor's said that, depending on the circumstances, it viewed "certain types of debt exchanges and similar restructurings as equivalent to a payment default".
The options laid out so far for restructuring Greek debt would constitute such a default, it said.
Shares in European banks lost ground following the downgrade.
In the UK, Royal Bank of Scotland and Lloyds Banking Group both lost about 2.3%, in France Credit Agricole and Societe Generale fell about 2%, while in Germany Commerzbank slipped 1.7%.
Last month, Standard & Poor's downgraded Greece to CCC from B.
Over the weekend, eurozone finance ministers approved the latest tranche of emergency help for the Greek economy.
They will release 12bn euros (£10.4bn, $17.4bn) in the next two weeks to help Greece meet spending commitments and avoid defaulting on its huge debts.
Last week, the Greek parliament passed tough austerity measures demanded by the European Union (EU) and International Monetary Fund (IMF).
MPs backed the measures despite angry protests on the streets of Athens.
Last May, the EU and IMF provided 110bn euros in emergency loans to Greece, and agreed last month to provide another 120bn euros in loans to try and help the country though its debt crisis.