The 6-year-old's body rejected the donated organ, Gulf News reported. She died in Amritha Hospital in Kochi, where the transplant was carried out last week.
Her father donated part of his liver in an effort to save his daughter.
Delna, who lived with her family in Kerala state in southwest India, was diagnosed recently with severe liver disease. Doctors said a speedy transplant was needed to save her life.
When a local newspaper publicized her situation, people from around the world donated a total of about 3 million rupees ($47,000). The state government provided 200,000 rupees ($3,000).
The family has a son who also needs medical treatment, Gulf News said.