The sum was announced last Friday by Sam Galbraith, the minister with responsibility for both health and children. It is part of a Pounds 43 million programme of "planned strategic developments" to target information technology, education and training in the National Health Service.
Mr Galbraith made the announcement at the Children in Scotland annual conference in Gourock last week. He said: "Services must be child-centred. My aim is that a child with multiple problems, such as cerebral palsy or cystic fibrosis, has their care designed around their needs and around a doctor's speciality.
"We must continue the drive to develop services that are combined within the NHS, and integrated with other agencies such as education, social work and the voluntary sector."
Health boards will be expected to come up with "ground-breaking ideas" and make competitive bids to the Scottish Office before they get any money. The Government wants to see "measurable outcomes".
The Pounds 3 million is intended to promote a system of "seamless care" for children through joint working, tackle inequalities in the health and care of children, and institute better networking across clinical boundaries.
The conference heard from a leading health specialist that "medicine and politics cannot and should not be kept apart".
Harry Burns, director of public health for Greater Glasgow Health Board, claimed that if wealth was more effectively distributed both the health and academic performance of the less affluent could be improved.
Dr Burns cited exam figures from Glasgow showing a clear link between poverty, as defined by the number of school meals, and the top, middle and bottom school performances in Standard grade.