The plan also calls for working with states to ensure that private health insurers cover treatment of the disorder, her campaign said.
"I want to help families do the work that they're already doing but which is so difficult" in taking care of family members, Clinton said at a campaign stop in Sioux City, Iowa.
"A lot of those families are just at their wits' end" finding services and figuring out how to pay for them, including as autistic children grow into independent, employed adults, she added.
Autism affects more than 3.5 million Americans, according to the Autism Society, an advocacy group.
The former US senator's plan comes on the heels of her proposal for dealing with Alzheimer's disease, the most common form of dementia.
Clinton has made helping the middle class a centerpiece of her campaign, and the health initiatives could help family caregivers, who can feel particularly stretched for time and resources.
In addition to a nationwide campaign to screen children for autism, Clinton would establish public-private partnerships to help autistic children move from school-based services to more independent lives, including employment opportunities.
Ari Ne'eman, president of the Autistic Self Advocacy Network - an organization run by and for autistic adults - praised Clinton's plan on a conference call organized by the campaign, including supporting people with the disorder as they lead their lives.
Autism, formally known as autism spectrum disorder, has become increasingly common in the United States, with the Centers for Disease Control and Prevention documenting a rise in its prevalence from about one in 150 children in 2000 to about one in 68 children in 2010.
However, some experts caution that the apparent rise could come as parents and doctors grow more aware about diagnosing the disorder.
While certain risk factors are known, including some chromosomal and genetic conditions, the exact causes of autism remain unknown.
Clinton, a former secretary of state and former first lady, is the front-runner for her party's nomination for the November 2016 presidential election.
She has support from 57 per cent of her party, compared with 31 percent support for her main rival, US Senator Bernie Sanders of Vermont, in a five-day rolling poll from Reuters/Ipsos dated December 29. Former Maryland Governor Martin O'Malley is also running for the nomination.