The drug law, called the Medicare Modernization Act, is to go into effect in January.
Families USA said the act will harm many of the 6.4 million lowest-income elderly and people with disabilities, who are known as "dual eligibles" because they receive both Medicare and Medicaid.
But beginning January, dual eligibles will be receiving drug coverage through the Medicare drug benefit rather then through Medicaid, the announcement said.
In order to help finance the new drug benefit, states will be required to pay the federal government most of the savings that they would realize from no longer having to provide drugs to dual eligibles in their Medicaid programs, the group said.
The act "creates a perverse incentive to cut the poorest of the poor off the Medicaid program because that is the only way states can reduce their payments to the federal government," said Ron Pollack, executive director of Families USA.