Doctors running the practice in Llanwrtyd Wells have written to Health Minister Mark Drakeford asking him to reconsider the scrapping of the Minimum Practice Income Guarantee (MPIG).
They say 1,200 patients will have to travel 13 miles to their main surgery in Builth Wells from August.
The Welsh government said there had to be "new ways of meeting local needs".
"Llanwrtyd Wells is a large rural town with a high proportion of elderly patients with complex medical problems," the GPs' letter said.
"Without a branch surgery patients could face numerous lengthy trips for even routine appointments," it continued.
"Travel would simply not be possible for some patients, especially in winter."
A Welsh government spokesperson said changes to the MPIG had been agreed with the British Medical Association's General Practitioner Committee for Wales.
"The solutions will lie in practices working together and with the health board on new ways of meeting local needs," the spokesperson added.
Alan Lawrie, director of primary care for Powys Teaching Health Board, said: "I am keen that we work with the practice to ensure that the health needs of the community are properly met and hope to be able to come to a suitable arrangement with them to ensure that this is the case."
Residents of a Powys town are alarmed that its only GP surgery is set to close due to a cut in NHS funding.