The Challenge had been helping to deliver the government-backed programme for 16- and 17-year-olds in London, the South East and the West Midlands.
However, the NCS Trust announced that it will not renew the contract from 2020 after a disagreement over a shared IT system.
The contract and the income relating to delivery of it was the principal funding source for The Challenge, according to its annual report.
In a joint statement, The Challenge's chairman, Bill Ronald, and chief executive Oliver Lee, said that the charity will continue its other work.
This includes HeadStart, a programme developed in partnership with the Mayor of London and employers, designed to bridge the gap between education and employment, as well as enabling young people to become socially active in their local community.
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"There will, naturally, now be a period of change at The Challenge as we refocus our energies and continue to explore new opportunities to achieve our ever more critical vision of an integrated society," they said, adding: "We will keep people fully updated as this evolves."
They also commented on the split itself, stating: "For several months we have been in discussions with the NCS Trust regarding NCS provision for 2020 and beyond.
"Regrettably we have been unable to resolve certain important contractual issues that adversely affect The Challenge's ability to operate on that future landscape.
"It is therefore with much sadness that we confirm from 2020 that The Challenge will no longer play a role in the delivery of NCS to young people across the UK.
"The Challenge has been at the forefront of NCS as its largest provider, delivering first-class, value-for-money NCS provision.
"It has played a critical and founding role in NCS for over 10 years from initial design of the programme to directly supporting over 242,000 young people to have a life-changing experience through it, and we are immensely proud of these achievements.
"Everyone at The Challenge wishes the very best to those now charged with delivering NCS to the young people of the UK.
We remain passionate advocates for NCS and stand ready to help in any way we can to promote and support this important work."
The trust said the decision resulted from being unable to reach agreement over the provision of a shared IT system "that ensures value for money, improves customer experience and protects young people's data".