Mehal gave the example of a story covering a match between two Algiers clubs, the headline of which read: "Today, even with Kalashnikovs, it will end badly".
The minister told the daily El Khabar newspaper: "We will stop the publication of newspapers that incite violence between Algerians."
He added: "I am not opposed to press freedom, quite the contrary -- I respect it, but there are limits to this freedom."
Director of the daily Planet Sport, Hamou Belahmar, said he found it "strange" that such remarks came from a minister who had worked as a journalist.
Algeria's dozen or so sports journals are massively popular.
The government promised at the beginning of May to increase press freedom, beginning with the decriminalisation of press crimes, while maintaining fines for offences relating to the president.
Abdelaziz Bouteflika has said he intends to introduce new legislation to replace the current laws, which date back to the 1990s.
A media regulation authority will also be created in plans currently being discussed with industry heads.