The letter, signed by Board president Ranbir Singh Mahendra, was addressed to ICC chief Ehsan Mani.
Mahendra confirmed that the missive had been sent, but refused to disclose the contents.
The letter is the latest move by the BCCI in its two-month standoff with the ICC over the ban handed out to Ganguly by match referee Chris Broad for the Indian team's slow over rate in the Ahmedabad One-dayer versus Pakistan on April 12.
It was learnt that the missive stated that the dispute was affecting the game of cricket and as such needed to be resolved as soon as possible.
The letter said the BCCI was seeking arbitration as per discussion in the ICC during the cricket world body's annual conclave last week.
It also reiterated the BCCI's consistent stand that there was no provision for banning a skipper owing to his team's slow over rate.
The ICC is likely to appoint an arbitrator in the matter in a day or two.
Ganguly, who has already served two of the six-match ban, earlier appealed to the ICC against the punishment. But the appeal was rejected by ICC appeals commissioner Michael Beloff.
The BCCI then notified the ICC executive board that it intended to dispute the process that was used to deal with the Indian captain's appeal under the ICC code of conduct.
Following this, the ICC had agreed that should the BCCI wish to take this matter further it must write to the ICC which would then refer this to the ICC disputes resolution committee.