The two hijacked jets that were flown into the World Trade Center towers in New York flew out of Logan.
The runway fire drill, announced on the airport's Facebook page, drew harsh condemnation.
The Massachusetts Port Authority, the agency that runs the airport, said in a statement that it "apologises for conducting the fire training exercise and understands that it may have offended many of those touched by the events of September 11."
"How clueless and insensitive can you be," one woman wrote on the airport's Facebook page.