The 27-year-old, who is currently recovering from a serious knee injury, received the suspension after being charged with 'multiple breaches of conduct'.
In a statement on its website, the FA said: "Dexter Blackstock has been suspended from all football activity for three months after he admitted multiple breaches of FA Rule E8 for misconduct in relation to betting.
"However, the Independent Regulatory Commission ordered that the player's
suspension be stayed until 31 May, 2016 and will only be automatically invoked
upon a proven breach of the FA Betting Rules during that period.
"Following the Independent Regulatory Commission hearing, Blackstock was also fined £60,000."
Blackstock, who signed a new four-and-a-half-year contract at the City Ground last season, last played for Forest in October before being sent out to Sky Bet Championship rivals Leeds United.
After four appearances for the Elland Road side, he suffered a season-ending knee injury in training and is not expected to return to action until October.