A section of the astroturf surface was singed when the pyrotechnic was thrown from the away support seconds after the final whistle of last month's William Hill Scottish Cup clash at the Falkirk Stadium.
Rangers won the match 2-0 with goals from Nicky Law and David Templeton but the result of the fourth-round tie was overshadowed by the flare incident.
The plastic pitch was only installed in the summer and Rangers have told the Bairns' directors that they will pay for the repairs.
Now they have also handed an "indefinite" ban to a 16-year-old female who has been charged for her "unacceptable behaviour".
A club spokesman added: "She will be banned from attending all home and away games following the flare incident at the [Falkirk] match.
"The club will continue to assist Police Scotland with their enquiries as they attempt to identify others who may have been involved."