Gaza health ministry spokesman Ashraf al-Kidra said one Palestinian was killed by the Israeli tank fire and Hamas confirmed the man belonged to the group.
"During the operation, Hamas detonated an explosive device at the forces, wounding five Israeli soldiers," said a military statement. "The soldiers were evacuated to an Israeli hospital. In an immediate response the soldiers opened fire and directly hit a terrorist."
The military announced last month that it had discovered the concrete-lined, mile-long tunnel dug from the Hamas-controlled Gaza Strip into Israel. It later said the tunnel opening "was discovered near Israeli civilian communities" and action was taken to demolish it and prevent further attacks.
Hamas has dug tunnels into Israel in the past. In 2006, Hamas-allied militants sneaked into Israel through one such tunnel, killed two Israeli soldiers and kidnapped a third, holding him hostage in Gaza for five years.
Hamas spokesman Sami Abu Zuhri "blessed" the latest attacks saying his group "gave a painful lesson" to Israel.
"Gaza will be the land of hell" for Israel, he said on Friday.
Israel and Hamas are bitter enemies. Hamas does not recognize Israel's right to exist, and since it took power in the Gaza Strip, thousands of rockets have been fired at Israeli communities.
Israel carried out major military operations in 2009 and last year in Gaza in response to the rocket fire.
While various militant groups operate in Gaza, Israel says it holds Hamas responsible. The sides largely have observed a cease-fire since last November.
Hamas has ruled Gaza since 2007 after ousting the rival secular Palestinian Fatah group in bloody street fighting. Fatah and the Palestinian Authority, led by Abbas, now govern part of the West Bank only.
After the Hamas takeover, Israel and Egypt imposed a blockade on the coastal territory. Israel has eased the blockade in recent years, but still restricts the imports of some goods into Gaza.
Since the summer, Egypt's military has tried to destroy or seal off most of the smuggling tunnels under its side of the border with Gaza, and accused Hamas of fomenting unrest in Egypt.
The move followed the popularly-backed coup that ousted Egypt's President Mohammed Morsi, from the Islamist Muslim Brotherhood group, a parent organization of Hamas.