The animal parts were packed in 16 sacks found in the animal export section, said Sambo Dangaladima, the customs controller at Murtala Muhammed airport.
He said the smell from the sacks aroused suspicion of the authorities.
The consignment is estimated to be worth 200 million Naira ($478,000; £416,000)
A suspect linked to the package is said to have escaped.
Nigerian law forbids export of donkey parts.