The military said it launched the operation on Wednesday morning near Khan Younis in response to shooting attacks and other anti-Israel activity in the area of the border fence.
The Israeli air force also conducted air raids in the area in support of the operation that the army said was aimed at preventing attacks near the barrier between Gaza and Israel.
On Tuesday, an Israeli missile attackin northern Gaza killed a member of the Popular Resistance Committees. Another two people were wounded in the strike at a cemetery east of the town of Jabaliya.
During Tuesday's operation, troops said they uncovered a tunnel shaft about 3.5m deep in a house near the border fence.
A similar tunnel was used by Gaza fighters who raided an army post on the border in June 2006 and captured an Israeli corporal, who is still being held by Hamas.
Since Israel and the Palestinians formally revived peace talks in November, at least 371 people have been killed, most of them Gaza fighters, according to an AFP tally.
At least 6,334 people have been killed since the eruption of the latest Palestinian uprising in 2000, the vast majority of them Palestinians.