Baby Fae, the month-old infant who set a record for survival with a transplanted animal heart, died tonight after living 20 days with the walnut-sized heart of a young baboon.

A short bulletin from Loma Linda University Medical Center said the dark-haired baby girl died there at 9 p.m. PST, several hours after her kidneys began to fail.

Doctors at the medical center 60 miles east of Los Angeles had been concerned since the Oct. 26 transplant operation about the effect an immuno-suppressive drug, cyclosporin A, would have on the infant's kidneys, but they had reported no adverse reaction until today. Last weekend, doctors had increased dosages of the drug to prevent another effort by the child's body to reject the alien heart.

University spokesman Edward Wines said doctors attempted artificially to cleanse the child's blood of waste after her kidneys began to fail but were defeated by the swift onset of heart failure. Emergency cardiac massage failed to revive the child, he said.

Doctors at the Seventh-day Adventist institution had planned five operations to transplant baboon hearts into children suffering from the same ailment as Baby Fae -- hypoplastic left-heart syndrome, a severe, nearly always fatal deformity found in newborns. They said, in addition, that they had considered transplanting another baboon heart or a human heart into Baby Fae if the original transplant failed, but Wines declined to explain tonight why this was not attempted.

Wines said doctors would present a more complete explanation of the circumstances at a news conference Friday.

The child, whose parents asked for anonymity, was born in Barstow, Calif., Oct. 14 with almost the entire left side of her heart missing. Her mother, who is separated from the child's father, was told by doctors at Fae's birth that the baby had little time to live. She took the child to a motel in order not to upset her 2 1/2-year-old son, but was persuaded by Loma Linda heart surgeon Dr. Leonard L. Bailey to allow him to try the experimental transplant.

Three other humans have received animal-heart transplants, the last in 1977, and none survived longer than 3 1/2 days.

Bailey, however, had succeeded in keeping a goat alive for 5 1/2 months with an implanted lamb's heart and argued that an infant with an underdeveloped immune system would be less likely to reject alien tissue than an adult