The 29-year-old Georgian has featured twice for the Blues since joining on a short-term contract.
In the second of those games, he bit Ospreys back-rower Rob McCusker and was sent off.
Peikrishvili's ban has been back-dated to 22 November and he is free to play from 2 January, 2017.
The former Agen, Castres, Brive and Bayonne prop made his Blues debut in their 62-25 Anglo-Welsh Cup defeat by Exeter Chiefs before the game against Ospreys.
Prior to joining Cardiff Blues, Peikrishvili was on a short-term contract with Ulster as injury cover, but did not appear for the province.
The Rugby Football Union judged the case as the competition comes under their jurisdiction.
The panel also banned Scarlets' back-rower Jack Condy for punching during their 36-21 win over Newport Gwent Dragons on the night Peikrishvili saw red.
Cardiff Blues prop Anton Peikrishvili has been banned for six weeks for biting an opponent in their Anglo-Welsh Cup defeat by Ospreys on 18 November.