The City Council passed a ban July 12 outlawing the sale or possession of semiautomatic rifles with pistol grips and detachable magazines.
The gun owners' organization had planned to hold its annual three-day event, expected to draw as many as 60,000 people, at the Greater Columbus Convention Center.
"The party is cancelled because last week your City Council unanimously voted to revoke the constitutional rights of law-abiding citizens in Columbus by banning perfectly legal firearms," NRA Executive Vice President Wayne LaPierre said.
City officials said the NRA had been told there was a potential for the ban.
"Public policy decisions - especially those affecting the safety of our citizens - cannot be influenced by any narrow interest group that happens to visit," Council President Matt Habash and councilman Michael Mentel said in a statement.
Federal lawsuits have overturned two previous attempts by Columbus to ban assault weapons. The latest law attempts to avoid that by spelling out a distinction between legal sporting weapons and military-style assault weapons.
The NRA also considered Portland, Ore., and Reno, Nev., for the 2007 event.