A statement posted on Udinese's website says the player was taken by armed men on Saturday morning outside Warri, the main city in the Niger Delta which is an oil-rich area where foreign firms pump 2.4 million barrels of crude a day.
Obodo's relatives told ANSA news agency that the kidnappers are asking for a ransom of $188,000.
Obodo's brother Kenneth, who plays for Pisa, says the family has been in touch with the kidnappers. He adds that Obodo is not in danger, but his family is concerned since they were only able to get $125,000 to free the player.
Lecce was relegated to second-tier league, while Udinese finished third in Serie A this season.