Hamas, which controls the Gaza Strip, described the target as "open ground" but witnesses said it was a building with two rooms and a courtyard.
An Israeli security source said intelligence indicated the tunnel had been dug by several Palestinian factions other than Hamas.
Earlier on Sunday, Hamas said that unidentified Palestinians had set off explosive devices at two of its security compounds in Gaza City.
Hamas said the attacks had targeted the Ansar-2 security compound and the Gaza residence of Mahmoud Abbas, the Palestinian president, who has stayed away from the territory since his Fatah faction was forced out by Hamas in 2007.
Hamas security sources said that they had defused a third bomb near what is known as the department for security and protection.
No one claimed responsibility for the attacks, while Israeli military sources denied involvement.
Ihab Ghussein, Hamas interior ministry spokesman, said they were investigating the explosions.