Existing volunteer-led initiatives with a proven record of supporting children, young people and families can apply for a portion of a £2m pot of funding so they can expand.
The Office for Civil Society (OCS) and charity Nesta are offering half of the money to projects that help young people manage their money, and families deemed to be "just about managing".
The Savers Support Fund will provide four to six grants of between £150,000 and £250,000 to enable organisations to expand and grow the support they currently offer, or replicate or franchise their models.
The remaining £1m is being offered to volunteer-led programmes designed to help parents of children aged up to four achieve developmental milestones.
Applicants for both funds must demonstrate their projects include a focus on digital, either by using volunteers who give their time online, or showing that they utilise an app or other digital technology to deliver outcomes.
Previous examples of digital schemes funded by Nesta include an online peer-to-peer support network for young people living with the HIV virus, and an online helpline for under-25s staffed by volunteers.
Minister for civil society Rob Wilson said volunteers were "invaluable, supporting communities and helping to build a shared society for everyone".
The application deadline for the funds is 29 March 2017. Projects that receive the grants will run from July 2017 until December 2018.
Nesta director Vicki Sellick said she hoped the funds would mobilise "thousands more" volunteers.
"The innovations we back to grow through these new funds will make a lasting difference in improving the chances of pre-schoolers in succeeding, and helping young people and adults in debt to learn lifelong habits of saving and money management," she said.
The projects should also support public services, as OCS and Nesta aim to encourage the use of volunteers in services such as early years settings and youth clubs.