In an interview with the Sydney Morning Herald, Shah hinted that it was possible that Malcolm Speed, the ICC's chief executive, might face an unprecedented no-confidence motion at the next meeting of the executive board in June.
"It is something we will discuss with our board," Shah said. "Some of it will depend on how other boards are feeling. It is fair to say that there are quite a few things to sort out at the next chief executives' meeting."
While the relationship between the ICC and the Indian board has been frosty, the stinging attacks on the way the World Cup has been organised may well turn out to be the watershed.
"We are not that satisfied," Shah told the newspaper. "It is becoming more and more bureaucratic. My board is of the belief that cricket is a simple, enjoyable game, but that is not how it appears at present.
"The ICC has so many staff members. It is unnecessarily employing so many people and that costs the other members. The ICC should move away from the bureaucracy and become more simplified. They should be concentrating more on the game."
Shah's comments were backed by Lalit Modi, the BCCI's vice-president, who called on Speed to be replaced by someone from Africa or Asia who "understands the problems of a majority of ICC members".