Responding to a consultation on the strategy, the NYA said that the covenant was needed to ensure the government is committed to investing in youth provision and ensuring young people have a say in political decisions.
Meanwhile, UK Youth has called for a long-term youth strategy, developed in partnership with young people and the youth sector.
The idea of a youth covenant bears similarities to a government commitment to introduce a Care Leaver Covenant - setting out the rights and services children leaving care can expect.
Plans for a Care Leaver Covenant were first announced in May 2016 and it was due to be introduced by October 2017, but is still in the process of being established.
The NYA said that a youth covenant fits with the civil society strategy's aim of creating a fairer society as it would help ensure young people's views are heard and respected.
It wants the covenant to also acknowledge the broad commitment needed across government, the charity sector, the community and business to support young people.
This should include supporting youth work, social and community action and developing young people's skills, the NYA said.
"When young people have their views heard and respected, it is a fairer society," said NYA chief executive Leigh Middleton.
"Therefore the NYA is calling for a youth covenant as a social contract with young people."
"This needs to include a positive commitment across government to our collective impact - statutory, voluntary, business and community - to invest in young people, their inclusion in decision-making and democratic engagement.
"To achieve this youth work can have a transformational role, empowering young people and bridging intergenerational divides.
"There is a recognition that we need to rebuild the infrastructure to develop and support youth work, embed social action and grow communities.
"That requires greater investment in youth work and youth services, for young people to be skilled and equipped to learn and earn, be active members of their communities, and be happy and confident in their future."
In its response to the civil society strategy, UK Youth calls on government to ensure it has a long-term strategy in place for young people.
"Through consultation with organisations and young people from across our network, we have submitted a comprehensive response that includes a call for the government to develop a clear, long-term strategic vision for young people, creating a clear comprehensive and inter-connected strategy in partnership with young people and the youth sector," a UK Youth spokeswoman said.
"Whilst we are disappointed that there is no funding related to the outcome of the civil society strategy we recognise the opportunity this consultation provides in shaping future spending reviews to prioritise investment in youth services and we call on government to work with UK Youth and our colleagues across the sector to explore how this can be achieved."
The government announced in November 2016 that it planned to create a youth policy statement setting out a "clear narrative and vision" for supporting young people.
The NYA's call for a covenant comes amid a backdrop of cuts to youth services in recent years.
Figures published by the House of Commons library last November, following a Labour Party request, found that council spending on youth services had been cut in half (53 per cent) over the previous seven years.