It is the second largest loan issued by the £125m investment fund, which was set up by the Government to help charities deliver public services.
The investment is structured as a loan of £4.7m and a grant of £284,000, which will help the units to cover their costs before they reach full occupancy. The loan is to be repaid over 16 years at an interest rate of 6 per cent.
The RNID plans to use the cash for four purpose-built residential mental health units, which will offer an alternative to hospital care for those who are deaf and in need of specialist mental health treatment.
"This project addresses a very important need," said Richard Gutch, chief executive of Futurebuilders. "Having a hearing impediment and a mental illness is a devastating combination.
"This is the sort of investment that is well suited to Futurebuilders. The RNID will be able to work with Primary Care Trusts, which will provide an income to help repay the loan."
Dr John Low, chief executive of the RNID, said: "The incidence of mental health problems among deaf people is much higher than average. Individuals are often discharged from acute care straight back into the community without intermediate rehabilitative or community-based support.
"This project will help to ensure that they have access to the appropriate care."