The monarch and the Duke of Edinburgh fed seven-year-old Donna while touring a new Â£2m home for nine Asian elephants at the Bedfordshire attraction.
They also met 10-month-old Elizabeth, born the day before the Queen's 90th birthday celebrations last year and named in her honour.
Both elephants live in the Centre for Elephant Care, a new custom-designed barn.
The barn, which has one-metre deep soft sand flooring, is set among 20 acres of paddocks for the herd.
Professor David Field, a director for the Zoological Society of London (ZSL), said the Queen was "absolutely delighted" to learn 72 stone (460kg) Elizabeth was named in her honour.
Assistant curator of elephants Lee Sambrook, who demonstrated how keepers clean the animals' feet and inspect their teeth, said the Queen was especially interested to hear about the round-the-clock care they receive and compared it to keeping horses.
Asian elephants are considered endangered due to habitat loss, poaching and human conflict.
The ZSL charity - which runs the zoo and of which the Queen is a patron - is involved in more than 50 conservation programmes to ensure elephants and humans can coexist peacefully.
The centre will open to the public on Wednesday.
The Queen fed an elephant a banana during a visit to Whipsnade Zoo.