Clashes are common on Fridays, with regular protests near the border in support of Gaza farmers who say troops uprooted their trees to create a buffer zone.
Emergency services chief Ashraf al-Qudra told AFP 13 protesters were wounded by gunfire and four hit by tear gas.
Earlier he said one of the men shot was in critical condition.
An army spokeswoman confirmed the shooting but did not say if anyone was hurt.
"Our soldiers tried to keep the crowd at bay by using anti-riot methods and by firing live bullets towards the legs of the main instigators," she added.
Later the army said that two "projectiles" fired from the Gaza Strip hit an open area in the southern Israel without causing casualties or damage.
It was not immediately clear if they were rockets or mortar rounds.
Tensions have risen in and around Hamas-ruled Gaza after a year of relative calm, with army figures showing at least 36 projectiles have been fired at southern Israel since the start of 2014.
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