Al-Haji Salisu Yunusa’s abduction led to the brief closure of the 80-year-old market in the south-eastern town of Ezamgbo, a BBC reporter in Nigeria says.
His kidnappers are believed to be demanding a ransom, our reporter says.
Some 200 donkeys are said to be slaughtered at the market’s abattoirs every day for human consumption.
Police spokesman Sylvester Igbo said efforts were being made to secure Mr Yunusa’s release.
The BBC’s Abdussalam Ibrahim Ahmed in south-eastern Nigeria’s Enugu city says he understands that the abductors are demanding 300m naira ($1.9m; £1.2m) in ransom.
It reopened later, as traders feared that its closure could cause tension and complicate efforts to secure Mr Yunusa’s release.
Buying and selling donkeys and donkey meat has been a thriving business at the market since it opened 80 years ago.
About 20 trailer-loads of donkeys are dropped off at the market daily.
Customers from other south-eastern states also travel to the market to buy donkeys and their meat, our reporter says.