The military said it had no knowledge of any injuries, saying the navy had fired in the air as a warning not to exceed a permitted fishing limit.
One young man was taken to hospital with "serious" injuries, medics said.
Under the terms of Israel's eight-year blockade of the Palestinian territory, Gaza's fishermen have the right to trawl the waters up to six nautical miles off the coast.
But fishermen have said the Israeli navy fires on vessels even before they reach that limit.
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Last month, two fishermen were wounded and four went missing after the navy fired on two boats off Gaza, with the Israeli military saying it had foiled a "smuggling attempt" between Gaza and Egypt.
Around 4,000 fishermen work in Gaza, but more than half live below the poverty line.
The waters off Rafah town straddling the Gaza-Egypt border have become an increasingly important smuggling route since Egyptian security forces destroyed a network of tunnels under the border.
The shootings highlighted tensions in and around the impoverished and densely populated enclave months after a fragile truce ended a bloody 50-day conflict between Gaza militants and Israel.
The international community has warned that without concerted efforts to rebuild the decimated Gaza Strip, violence could erupt again, possibly within months.