Prosecutors say the 63-year-old Berkley Heights resident was seated next to the woman on the Continental Airlines flight.
Authorities say Advani reached under her blanket and sexually abused her.
Authorities say two passenger seated behind the pair observed what was happening and kicked the woman's seat to wake her. The woman awoke and alerted the flight crew.
Advani was detained when the plane landed in Newark on Friday.
An initial court appearance is scheduled for Monday afternoon.
It is not known whether Advani has retained a lawyer.