A spokesman said it was the longest tunnel found to date and was meant for use in attacks on Israeli civilians.
The military wing of Hamas, which governs the Gaza Strip, dismissed the find, saying the tunnel was not new.
The tunnel is longer than one which Israel announced it had discovered last October which reached 1.7km (1 mile).
Militants have repeatedly tried to penetrate Israel using tunnels under the heavily secured border, managing to use one in a raid which killed two Israeli soldiers and saw a third, Gilad Shalit, kidnapped in 2006.
The Israel Defense Forces (IDF) did not say when or where the latest tunnel was found, but that it had thwarted a potential attack.
"This advanced tunnel was intended to pose a direct link and threat to Israeli territory, and enable Hamas terrorists to reach and harm Israeli civilians," said spokesman Lt Col Peter Lerner.
"Tunnels such as this are built to assist terrorists in the execution of terror attacks.  In the past Gaza terrorists have utilised such tunnels to Israel for infiltration, detonation and abduction of Israeli citizens."
The IDF said it was still investigating the tunnel, which it said ran for hundreds of metres inside Israel - without giving a precise figure.
However Hamas' military wing, the Izz al-Din al-Qassam Brigades, disputed Israel's claim.
A spokesman noted "there was no military or intelligence achievement by the enemy", adding that "this tunnel is not new.
"It is an old tunnel that Israel exposed two months ago and jihad fighters worked to rebuild it."

It follows the revelation that the Church of England has dropped its opposition to gay clergy becoming bishops if they agree to stay celibate.
The Reverend Martin Reynolds says his friend Jeffrey John, the Dean of St Albans, has been made a "whipping boy" in the row.
He told Radio Wales it would be great if he could now become a Welsh bishop.
Dr John, from Tonyrefail in Rhondda Cynon Taf, has been at the centre of the row over gay bishops having twice been put forward for the role in the Church of England.
In 2003 he declined the position of Bishop of Reading in the face of protests from traditionalists.
He was also rejected as a candidate for the Bishop of Southwark in 2010, with evidence emerging it was because of his sexual orientation.
On Friday, however, it was revealed that after a decision taken last month the Church of England would allow gay men in civil partnerships to become bishops as long as they promise to be celibate.
Unlike the Church of England, the Church in Wales has never had a ban on gay clergy in civil partnerships becoming bishops.
Mr Reynolds, an Anglican priest in Newport, claimed the reason the moratorium in the Church of England was introduced 18 months ago was because Dr John was about to become Bishop of Southwark.
He told BBC Radio Wales: "Rowan [Williams, the former Archbishop of Canterbury] didn't want another furore ... they shafted Jeffrey yet again - introduced this rule that you couldn't be in a civil partnership which of course Jeffrey is with Grant [Holmes, a hospital chaplain].
"Poor old Jeffrey's been more than just a whipping boy - he's been assassinated really several times."
Asked if there was now any realistic chance of his friend becoming a bishop in the Church in England, Mr Reynolds said: "Wouldn't it be nice if he became a bishop in the Church in Wales?"
He added that gay clergy in civil partnerships in Wales are not asked "if we do anything naughty in bed".
Asked about the question of policing the celibacy of gay clerics, Mr Reynolds said he believed honour still exists in the church.
"When Jeffrey said he and Grant weren't actually sleeping together anymore I think we all believed him.
"I don't think there was a single person ... that I ever spoke to said Jeffrey wasn't telling the truth."
Mr Reynolds also praised the Church in Wales approach on the celibacy issue.
"In Wales we've never bothered, we've never tried," he said.
"Our bishop has never introduced any such a role and, of course, we know that the archbishop of Wales has said if there was a gay man who was in a relationship who was nominated, he'd be happy to ordain him."
The Israeli military says it has uncovered a tunnel dug by militants from the Gaza Strip which runs hundreds of metres under Israel.
[NEXT_CONCEPT]
A gay rights campaigning clergyman has called for a leading Welsh gay cleric to be made a bishop in Wales.