Two Palestinians approached the Gaza-Israel border fence on Friday afternoon, and one suspect climbed over the fence, ignoring calls by the IDF to stop.
Soldiers fired on the man's legs, striking and injuring him.
The suspect is in IDF custody.
A rocket siren sounded earlier in the Ashkelon Coast Regional Council earlier was a false alarm, the IDF said.
Residents in the area did not report hearing an explosion. The siren may have been triggered by small arms fire detected by the system.
In a separate incident, Israel Navy forces shot at Palestinian fishing boats by the northern shore of the Gaza Strip, according to Palestinian media reports.
Gaza residents reported hearing gun shots off the coast of Gaza City, but no one was injured in the incident.
The IDF spokesperson office said that the soldiers fired warning shots into the air when the boats strayed from the 6-mile fishing zone.
The incidents come after a shooting incident along the border between the Gaza Strip and Israel, in which a soldier was seriously wounded by Hamas fire and a top Hamas activist was killed when IDF troops fired back.
Gaza-based militants on Wednesday opened fire at an IDF patrol, an event which security sources said was not likely a planned assault.