A second offence will lead to an automatic minimum ban of 10 games in measures agreed at the FA's annual general meeting on Thursday.
Clubs can also be charged if two or more of their employees are sanctioned for discriminatory abuse in any 12-month period. The punishments will apply to other types of discrimination including religion and sexuality.
"Football is about inclusivity and we want everyone to be able to play the game in a safe and welcoming environment," FA chairman David Bernstein was quoted as saying by the BBC.
"We have consulted far and wide and the new sanction and education package has been agreed by all partners involved in the process, including the Professional Footballers' Association, the League Managers' Association, Premier League, Football League, referees and [anti-racism group] Kick It Out."
However, the measures fall short of UEFA's proposed minimum 10-game ban for incidents of racial abuse in its competitions.
The FA reviewed its sanctions for racial abuse in the wake of high-profile cases involving Chelsea defender John Terry and Liverpool striker Luis Suarez.
Terry was banned for four matches and fined £220,000 for racially abusing Queens Park Rangers defender Anton Ferdinand in October 2011, while Suarez received an eight-game suspension and a £40,000 fine last season for abusing Manchester United's Patrice Evra.
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