The border troops shot the 23-year-old man "in the back and the bullet settled in the heart. He died on the spot," emergency services spokesman Ashraf al-Qudra told AFP.
The shooting was confirmed by the spokesman of the interior ministry in Gaza, Iyad al-Bazm, in a message on his Facebook page.
"A Palestinian citizen, aged 23, was killed by Egyptian army fire on the Egyptian-Palestinian border and the security agencies are investigating the incident to find out the motives," it said.
The man, whose identity was not revealed, is the first Palestinian "to have been killed in a long time" along the border between the Gaza Strip and Egypt, according to Qudra.
On Tuesday, Egypt announced that work to double the width of a buffer zone along the Gaza border would begin next week to prevent militants infiltrating from the Palestinian enclave.
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Construction of the 500-metre (546-yard) buffer zone along 10 kilometres (six miles) of the border follows an October 24 suicide bombing that killed 30 Egyptian soldiers. Some 800 homes are being demolished in the process.
After that incident, Egypt declared a three-month emergency in parts of North Sinai, a remote but strategic region bordering Israel and Gaza, and closed the Rafah border crossing for two months.
Egypt reopened the crossing for two days in November and again in December, for three days, to allow people stranded in Egypt to return to the Palestinian enclave and for Gazans to leave.
The Rafah crossing is Gaza's only gateway to the outside world not controlled by Israel.
Egypt suspects Palestinian militants of aiding jihadist attacks against its security forces that have increased since the army ousted Islamist president Mohamed Morsi last year.
The Egyptian army has also stepped up the destruction of tunnels from Gaza it says are used to smuggle arms, food and money by Palestinian militant group Hamas which controls the territory.
Cairo says it has destroyed more than 1,600 tunnels since Morsi's ouster.