Police in Cross River state said those arrested included the baby's mother, who said extreme poverty forced to sell her child for around $90 (£60).
Correspondents say the issue of so-called baby factories is still prevalent in the region.
In 2013, 17 pregnant teenage girls and 11 babies were rescued from a house in the south-eastern state of Imo.
Local police told the BBC Hausa service that they have opened an investigation.
Six people have been arrested in south-eastern Nigeria for allegedly selling a two-week old baby.