The three-year-old boy, named by Ugandan media as Elisha Nabugyere, was the son of female ranger Doreen Ayera, who works at Queen Elizabeth National Park.
Ms Ayera had left the child in the care of a nanny at the unfenced staff headquarters of the Mweya Safari Lodge, Ugandan news site the Daily Monitor reports.
Wildlife authority spokesman Bashir Hangi said the child had followed the nanny outside the main house and towards a kitchen.
He said a leopard was hiding nearby and mauled the toddler before dragging him to a bush at about 9pm on Friday.
Mr Hangi said: “The rangers immediately swung into action (and) searched for the baby but they found only a skull in the morning under a tree.”
He says rangers are hunting the leopard because it now has a taste of human blood and may want to kill again.
Mr Hangi said: “The maid was not aware the child followed her.
“She heard the kid scream for help, she intervened but it was too late.”
The Queen Elizabeth National Park in southwest Uganda has one of the highest populations of predators such as lions, leopards and hyenas in the country.
Rangers are employed to live within the grounds to protect the animals from poachers.
The park, which covers an area of 1,229 sqaure miles, is one of Uganada’s top tourist hotspots.