Sessions ranging from art therapy, sport and gardening will be provided to 20 men at the prison.
Until now, prisons have opted for more traditional care services to meet the physical and mental needs of inmates.
The first course will start this month, and could be followed be a larger project aimed at improving health and wellbeing, and reducing reoffending.
Social prescribing – referring people to a range of local, non-clinical services – is already available to patients registered with a cluster of GP surgeries in Swansea.