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"I didn't realize I was causing the woman any distress until she woke me up with a quick hit to the chest," Aiken tells Entertainment Tonight.
Neither the 2003 American Idol runner-up nor the unnamed female passenger was charged in the incident, though both were questioned by the FBI.
Aiken, 28, was on a Saturday morning Continental Airlines flight to Tulsa International Airport to perform that evening at the Brady Theater in Tulsa.
"While sleeping on a plane over the weekend, my foot evidently found a home on the arm rest of the passenger seated directly in front of me," Aiken tells ET.
He adds: "Unfortunately, being that this happened on a plane, the FBI was called in to investigate and eventually we were all sent on our way. I'd like to thank everyone for their concern; I am fine and have taken steps to prevent any foot wandering in the future."
Special Agent Gary Johnson, spokesman for the FBI in Oklahoma City, tells PEOPLE: "No one was charged or taken into custody nor is that anticipated." He added that both passengers complied with instructions by the flight crew.
"This was a very minor incident. And it was well-handled by the flight crew," he said.
• With reporting by JUDY RAKOWSKY
