The Israeli army confirmed that in two separate incidents early on Friday, soldiers spotted Palestinian men laying devices near a border fence and opened fire, hitting three of them.
An army spokeswoman said one man was being questioned.
There was no claim of responsibility from any Palestinian organisation.
The incident was the latest in a series of clashes between the Israeli army and Palestinian fighters in the past week.
Later in the day, Israel's air force fired a missile at a Palestinian car.
Palestinian witnesses reported a car had been partially destroyed in the attack. Two people were wounded in the missile strike in the northern Gaza town of Bait Hanun.
Israeli soldiers killed at least five Palestinians on Thursday during a raid in the occupied West Bank city of Nablus.
The raid was the army's biggest since the Islamist group Hamas won parliamentary elections last month.