She was born a week ago, weighing 10.3oz, the smallest of the children.
All the babies, born from 8 December to 20 December to Nkem Chukwu and her husband, Iyke Louis Udobi, are in intensive care.
Odera whose full name means "God has my life" was the fifth of the children to be born but her condition began to deteriorate on Saturday. She was moved from a ventilator to an oscillator to improve her blood oxygenation, but her heart began to fail, despite the efforts of doctors.
"We are very saddened by the passing of our beloved baby Odera," said the parents in a statement through the hospital.
"She is now safe with God in Heaven and we remain most grateful to Him for having blessed our lives with hers."
The other babies are also in critical condition and the youngest, Gorom, is recovering from abdominal surgery. Two babies - Ebuka and Ikem - remained on ventilators yesterday, but four others - Chidi, Echerem, Chima and Jioke - were breathing on their own.
Mrs Chukwu, who had taken fertility drugs, was in a stable condition yesterday. She has managed to visit her children.Reuse content