France captain Manaé Feleu has also appealed a suspension after being given a three-match ban for a dangerous tackle.
Both players, if the bans stand, will miss Saturday's World Cup semi-final against England and the final or bronze final.
Berthoumieu's admission occurred in a foul play review hearing. The panel said she accepted her bite was worthy of a red card and the off-field citing was warranted.
No action was taken against her on the field at the time.
Wafer accused Berthoumieu of biting her arm during France's 18-13 win on Sunday in Exeter. The referee referred it to the Television Match Official to review footage.
World Rugby said in a statement, "In reviewing the matter live, the TMO was unable to determine clear and obvious foul play and did not have the benefit of additional evidential submissions to corroborate."
For a sanction, the panel started the suspension at 18 games and deducted six.
"Although the player acknowledged the foul play and was remorseful, full mitigation was not given due to the seriousness of the player's actions, and that the player had the opportunity not to continue with the action," World Rugby said.
A 12-game suspension prevent Berthomieu from playing to March 1.
Feleu, leading Les Bleues at her second World Cup, was cited for a dangerous tackle that wasn't sanctioned on the field. At her hearing, she accepted there was foul play but didn't believe it was worth a citing.
But the panel found her guilty of head-on-head contact at speed with no mitigation.
Both appeals will be heard on Tuesday.
