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."
The Israeli military says it has uncovered a tunnel dug by militants from the Gaza Strip which runs hundreds of metres under Israel.