The foundation is part of the #WeRaceAsOne diversity initiative that F1 launched earlier this week, which followed on from a commitment made in November.
F1 says that the role of the new foundation will be "to finance primarily, but not exclusively, internships and apprenticeships within F1 for underrepresented groups to ensure they have the opportunity to fulfil their potential and have access to a promising career in the sport".
The foundation, which does not yet have an official name, will operate alongside the new "task force" that F1 announced this week.
Elaborating on the plans, F1 says that the latter "will be established over the next few months and will include input from the drivers and teams, as well as external diversity and inclusion experts.
"The Task Force will be specifically focussed at identifying the employment and education opportunities for underrepresented groups across F1, including STEM [science, technology, engineering and mathematics] careers, and the required actions to address these findings."
F1 says that the initial $1m donation from Carey is just the start of a fund-raising programme: "We hope that the funding will grow over time to support more interns and scholarship opportunities in the future.
"We believe that as a truly international sport we can make a difference by using our voice and determination to address these vital issues.
"We are a sport that represents millions of global fans and we must ensure we are as diverse and inclusive in our own community as the communities we serve around the world."
Carey stressed the importance of opening up the sport to people of all backgrounds.
"We fully recognise that F1 needs to be more inclusive and diverse," he said. "While we set out our strategy last year to improve the position of our sport, we need, and want, to do more.
"That is why we will establish a Task Force to listen and ensure the right initiatives are identified to increase diversity in F1.
"We want to ensure we give people from all backgrounds the best chances to work in F1 regardless of their gender, ethnicity, sexual orientation, or physical abilities.
"We are therefore also taking the initial step of creating a foundation to support key educational and employment opportunities across F1 that will give underrepresented talent the chance to work in this incredible sport and build an exciting career."