The mummy of a child of about two years of age is only 30 cm (12 in) tall and sits wrapped in blankets.
Bolivian police seized it two years ago from a woman who was going to ship it to France.
Experts determined it was an original but found that one of its legs had been added later presumably by the smugglers who wanted to raise its value.
Experts have not been able to determine the sex of the mummy but archaeologists think it came from a pre-Inca culture of coastal Peru.
Bolivian Culture Minister Pablo Groux handed the mummy to his Peruvian counterpart Luis Peirano at a ceremony at the Peruvian Foreign Ministry in Lima.
The two ministers also signed an agreement to improve their co-operation in the fight against the smuggling of cultural artefacts.
Referring to an increase in the illegal trade in antiquities, Luis Peirano said the mummy was “just a sample of the sacking, of the violation of our patrimony and all our inheritance.”
Peru, at the centre the Inca culture and other civilizations predating the Incas, has had thousands of its relics plundered and stolen over the centuries.
Peruvian officials say trafficking in mummies has been less common, though “lately, there has been an increase in the trafficking of human remains”.
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