It said the downgrade of the ESM and the EFSF, which were created to stabilise the euro zone by providing financial assistance to euro area member states in difficulty, was prompted by the high correlation in credit risk among the rescue funds and their largest financial supporters.
Moody's stripped France of its prized triple-A badge this month, cutting the sovereign credit rating on Europe's No 2 economy by one notch to Aa1 from Aaa.
It cited an uncertain fiscal outlook and deteriorating economy.
"Moody's view that there is a high correlation in credit risk among the entities' supporters is consistent with the evolution to date of the euro area debt crisis and the close institutional, economic and financial linkages among the major euro area sovereigns," Moody's said.
The agency said it kept a negative outlook for the new credit rating.
The EFSF and ESM said in a statement late on Friday that they took note of Moody's decision but did not agree with it.
"We disagree with the rating agency's approach which does not sufficiently acknowledge ESM's exceptionally strong institutional framework, political commitment and capital structure," said Klaus Regling, managing director of the ESM and chief executive of EFSF.
Moody's had announced it would review the Aaa rating of the two funds after the downgrade of France.
The euro pared most gains versus the US dollar in late Friday trade after Moody's downgrade.