Medical Service Ministries (MSM) is to transfer its resources to another Christian medical charity, the UK-based PRIME Partnerships in International Medical Education group.
The organisation, which has equipped missionary families with training to use first aid kits, says the decision reflects how "healthcare has developed worldwide."
Operating until 1996 under the name of the Missionary School of Medicine, MSM was founded in 1903 to equip missionaries in Africa, the Far East and South America with a basis understanding of medicine.
The training was provided by staff at the London Homeopathic Hospital and those from other medical institutions.
Modern medical advances such as the arrival of antibiotics and improving health services in the developing world saw demand for its help fall significantly during the latter half of the 20th centry, the MSM has said.
The school closed in 1996 but MSM began a grant-making trust, helping Christian health workers pay for their own training.
In a statement, MSM said: "PRIME has a unique ministry of training healthcare leaders from across the world to recognise the importance of providing not simply physical care, but care founded on a thorough respect for each person - each patient - as an individual valued by God and therefore deserving of compassionate and holistic care by the health personnel attending them, recognising - as the World Health Organisation does - the importance of the spiritual and mental dimensions to physical well-being.
"This echoes the ethos that brought MSM into being and sustained it throughout its 113 years, and is the reason that MSM has already, through grants over several years, partnered with PRIME. MSM wish PRIME well as they develop their vital work yet further."