Maxwell Berry, 22, was taken into custody at Miami International Airport on Sunday on battery charges, NBC reported, citing an arrest report.
Reuters could not immediately confirm details of Berry's arrest.
Berry is accused of groping the breasts of one flight attendant, touching the buttocks of second and punching a third in the face, according to the network.
Following that altercation Berry was subdued with the help of other passengers and duct-taped to his seat, NBC reported.
"Frontier Airlines maintains the utmost value, respect, concern and support for all of our flight attendants, including those who were assaulted on this flight," an airline spokesperson said in a statement released to NBC.