Fortune signed a two-year deal at the DW Stadium in July after leaving West Brom.
The punishment relates to a breach of the FA's Football Agents Regulation C10(a)(i), which states an agent "must not carry out any activity for or on behalf of a club in any transaction in respect of a player where the agent has carried out any activity for or on behalf of another club in respect of the same player in the immediately preceding completed transaction or contract negotiation of that player".
The striker's agent Willie McKay has also been punished by the FA, having his overseas agent registration suspended for nine months.
An appeal could see the Scot's ban overturned and in any case it will not come into effect unless he offends again in a two-year period.
Fortune has made 48 appearances in all competitions for Wigan this season, scoring five goals.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.