Canover Watson was questioned last month by police anti-corruption and financial crime units in his native Cayman Islands. He denies wrongdoing.
FIFA said on Tuesday that audit committee chairman Domenico Scala "decided to temporarily relieve until further notice Canover Watson, to whom the presumption of innocence applies."
The eight-member panel is next scheduled to meet on Dec. 16 in Morocco, on the sidelines of the Club World Cup.
It was formed in 2012, and scrutinizes FIFA's $1 billion-plus annual revenue and commercial contracts. Scala's team has intervened to block some of FIFA's 209 member federations applying for development grants.
Watson is a director of the Cayman Islands Stock Exchange and treasurer of the islands' football federation. He is a close associate of federation leader Jeffrey Webb, a FIFA vice-president and president of CONCACAF.
FIFA said the police investigation was not linked to Watson's work in football.
"After a preliminary clarification of the facts of the case and the allegations of the Cayman Island investigating authorities against Canover Watson, no connection with football and/or his role at association level has been established at this stage," football's governing body said in a statement.
Local media reported the case involves a 2010 contract to supply public hospitals with swipe-card billing technology.