The prize, launched in 2000, is awarded annually to an African writer of a short story published in English.
The prize was announced at a dinner held at the Bodleian Library in Oxford.
The winning story, set in the Eastern Cape, explores how traditional beliefs are used to tackle schizophrenia.
The judges said it was a “gracefully narrated” tale that left the reader “full of sympathy and wonder”.
Lidudumalingani will be given the opportunity to take up a month’s residence at Georgetown University as a Writer-in-Residence at the Lannan Center for Poetics and Social Practice.
“Memories We Lost,” explores mental health through the relationship of two sisters in a South African village, one of whom is schizophrenic and the other her protector. The sister’s situation deteriorates as her care is entrusted to Nkunzi, a local man who employs traditional techniques to rid people of their demons.
In addition to a $15,000 prize, Lidudumalingani will also be invited to speak at the Library of Congress and receive invitations to take part in Cape Town’s Open Book Festival, Nairobi’s Storymoja and Nigeria’s Ake Festival.