Tejarat Emrouz news, The Israeli military said it responded to the shooting with tank fire, targeting Hamas posts in the northern Gaza Strip. Gaza health officials said three Palestinian farmers were wounded.
Following their talks, the Israeli Defence Ministry announced a series of what it described as "confidence-building measures" that would ease the entry of hundreds of Palestinian business people to Israel.
There was no immediate claim of responsibility for the shooting attack from Gaza, which the Israeli military said slightly wounded the civilian. The border has been largely quiet since an 11-day war between Israel and Gaza militants in May.
Gantz, in his summation of the meeting on Twitter, made no mention of a peace process, stalled since 2014 after U.S.-backed talks collapsed. Palestinians seek to establish a state in the West Bank and Gaza Strip, with East Jerusalem as its capital.
"We discussed the implementation of economic and civilian measures, and emphasised the importance of deepening security coordination and preventing terror and violence - for the well-being of both Israelis and Palestinians," Gantz wrote.
Israel's multi-party government is deeply divided over the statehood issue. Palestinian rivalries remain strong, with Hamas, which has fought four wars with Israel, running the Gaza Strip.
In a move that could ease travel for thousands of Palestinians, the Defence Ministry said Gantz approved registration as West Bank residents for some 6,000 people who had been living in the territory, captured by Israel in a 1967 war, without official status.
Another 3,500 people from Gaza would also receive residency documentation, the ministry said.
The meeting followed several Palestinian attacks on Israelis in recent weeks in the West Bank and East Jerusalem. Palestinians also complain of attacks by Israeli settlers.