The cash will pay for 32 places.
Milton Keynes is served by six special schools but as the city grows, the council is anticipating more demand for additional specialist places for children with Social, Emotional and Mental Health needs (SEMH).
Proposals are now being considered to expand Stephenson Academy, an existing special school in Stantonbury with four new classrooms plus intervention and therapy spaces to help 32 pupils.
In a recent informal consultation the proposals received universal support from parents and other participants.
A decision to confirm the proposed investment is set for June 23.
In the past eight years, MK Council has opened six new schools and expanded 24 others, creating thousands of new school places.
The development of Stephenson Academy is proposed alongside an expansion of the age range to include Key Stage 2 pupils at the school.
Councillor Zoe Nolan, Cabinet member for Children and Families, said: "This critical project will allow the school to offer additional school places for pupils with special educational needs. As the city expands, we must ensure that no young people are left behind and that our network of local schools continues to support all families. Developing existing provision, alongside building sustainable new schools will remain a priority for this council.”
The project will be funded from the Council’s Special Provision Fund, a grant allocated to the council directly from the government.