The Create Open Health initiative is being led by Creative England with successful applications offered access to investment, technology expertise as well as marketing and sales support to develop their idea.
Ideas at the concept stage as well as those in need of further development are being sought, from UK-based individuals and organisations.
Using technology to help schools and parents spot mental health problems at an early stage is among issues the initiative is looking to cover.
Other areas include addressing social exclusion and helping young people manage mental health issues and improve access to care and information.
Technology and digital products that can tackle stigma associated with mental health are also sought.
Also involved in the initiative are health research organisation the Wellcome Trust, the West of England Academic Health Science Network (AHSN) and Bristol and South Gloucestershire based young people's mental health support charity Off the Record.
"We are looking for ideas that directly support and empower children and young people, their caregivers or their community, and the healthcare industry is the perfect place for us to start," said Creative England investment manager Tim Evans.
"As many in the industry know, one in 10 children between five and 16 years old have a diagnosable mental health problem and yet just 0.7 per cent of the NHS budget is spent on children's mental health.
"With this programme, we hope to tap into the vast wealth of knowledge and experience of our healthcare industry and help develop solutions that can have a real impact on the mental wellbeing of children and young people in the UK."
The deadline for submissions is midnight on 31 March 2019.
Current digital and technology initiatives that are supporting children's mental health include Mind Moose, a digital game that teaches children about mental health and helps them improve their resilience and emotional wellbeing.
Another is Neuro Champions, a progamme by Chanua Health that uses technology such as virtual reality to teach young people about their mental health.
Both are among technology initiatives to receive backing last year from a partnership between The Children's Society and investment organisation Bethnal Green Ventures.