Calling it "a day of freedom to travel," Spirit CEO Jacob Schorr said, "The sky should be full of Americans on that day. This will show that we're not a nation that can easily be brought down."
He said he hopes other airlines will follow suit.
Spirit has 90 scheduled flights with more than 13,000 seats on Sept. 11, a typical number for a weekday, Schorr said. Bookings for that day were already down for the Fort Lauderdale-based airline, but customers who already paid for tickets will get credit for a future flight.
Travelers can take as many flights as they want on Sept. 11, but tickets must be reserved by Sept. 8. If the second leg of a roundtrip flight is on another day, there will be no one-way penalty -- the cost will be half of the roundtrip fare.
Schorr estimated the giveaway will cost Spirit around $500,000.
"This will give people who otherwise couldn't afford it a reason to fly," Schorr said.
Spirit Airlines serves Fort Lauderdale, Fort Myers, Tampa, West Palm Beach, Orlando, Atlantic City, N.J., Oakland, Calif., Myrtle Beach, S.C., New York, Chicago, Detroit, Denver, Los Angeles, Las Vegas and San Juan, Puerto Rico.