The defender was found guilty of influencing "a football betting market" by deliberately getting himself booked in the FA Cup matches against Ipswich Town and Burnley last year, reports PA.
Two people known to Wood are said to have placed bets on him picking up the yellow cards in the games in question, punts which were "atypical in the context of the caution betting market".
The winnings those bets brought in reportedly amounted to around £10,000.
Wood, who now plays for Alfreton Town, has been fined £3,725 and ordered to pay costs of £1,550, in addition to being banned until March 8, 2024.
"The gravamen of the case against Mr Wood is that he planned to be cautioned, told personal acquaintances of that plan so that they and others to whom the information was passed placed bets," said the FA in a written judgement.
"The data supplied by betting organisations has revealed what is said to be unusual bets being placed on Mr Wood being cautioned in both matches. Two of those placing the bets are said to have close personal involvement with Mr Wood."
Wood denied the charges but was found guilty by an FA tribunal.