Mohammed Abu Zaida, 18, was shot in the neck and Mohammad Qita, 26, was hit in the stomach, ministry spokesman Ashraf al-Qudra said.
Fifteen other Palestinians were wounded by Israeli fire during the clashes east of the Bureij refugee camp in central Gaza, he said.
The Israeli army confirmed it had fired on protesters after they breached the "buffer zone" along the border.
"Dozens of rioters have breached the buffer zone and are attempting to damage the fence," a spokeswoman said.
Israel and the Palestinian territories have seen a wave of violence in recent months, with 23 Israelis and 154 Palestinians killed since October 1.
Most of the Palestinians have been killed carrying out attacks, while others were shot by Israeli forces during protests and clashes.
An American and an Eritrean have also died in the violence.
Fridays are known as a day of protest across the Palestinian territories.
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
