The French defender has not played for Los Che since the 3-0 Europa League defeat to Swansea, in which he was sent off.
Rami went on to publicly criticise manager Miroslav Djukic and his team-mates in the aftermath of that loss.
The 27-year-old Frenchman was subsequently temporarily suspended from the Valencia squad last week and disciplinary proceedings were opened against him following the comments he made in a radio interview.
After seeking legal advice, Rami on Friday morning held a meeting with Valencia officials in which he ''expressed regret'' for the statements, and the Primera Division club confirmed his punishment.
A statement published on valenciacf.com read: ''Valencia Football Club and Adil Rami, along with their lawyers, have held a meeting this morning in relation to disciplinary proceedings opened by the club against the player last week.
''After listening to the player, who has expressed regret for the statements made against the coach and his team-mates, the club have taken the mitigating factors into account and have decided to punish the player with a week of suspension without pay, in accordance with internal regulations."
Without Rami, Valencia have won four games in a row in all competition, including Thursday's Europa League win at Kuban Krasnodar, and have climbed to sixth in the Primera Division table.
Djukic is expected to rotate his squad following the win in Russia, with defender Jeremy Mathieu in line to make his 100th appearance for the club, while Oriol Romeu, Jonas and Ever Banega are also in contention.
Fifth-placed Bilbao, who are coached by ex-Valencia boss Ernesto Valverde, were beaten at Granada last time out and are set to be without Aritz Aduriz, Kike Sola and Mikel Balenziaga through injury, although Ibai Gomez could return from a thigh problem at the new San Mames stadium.