On Friday it emerged that the game's governing body wanted to speak to the 61-year-old over claims he broke rules by betting in a competition Tranmere were involved in.
Moore took charge of Tranmere on Saturday in the 2-2 draw at Bristol City, and conducted his press conference on Monday ahead of the game at Crawley on Tuesday night.
However, the Sky Bet League One club issued a statement on Monday evening which said they were suspending Moore until the conclusion of the FA's probe.
A statement from Tranmere on the club's official website read: "Tranmere Rovers have today announced that with immediate effect manager Ronnie Moore has been suspended until the conclusion of a Football Association investigation into a potential breach of betting rules.
"Assistant manager John McMahon has been placed in temporary charge of first-team affairs.
"The club will be making no further comment until the outcome of the investigation."
Source : PA