The One Direction star made the comment to a group of devotees who had gathered to meet him at the airport, and the video was later posted online.
The fans who uploaded the clip claimed that Horan made the comment as "banter", but Horan has now taken to Twitter to say sorry.
"Really sorry if I caused any offence," he wrote. "It was just banter with fans who I think of more as mates."
Horan added: "But I understand that it's not a word I should be using at all."
One Direction recently completed their 'Up All Night' tour in the US but will return to America for a show at Madison Square Garden in December.
Watch the video of Horan speaking to fans at the airport below: