The left-back collided with the attacker during Chelsea's 3-2 win at St Mary's on Saturday but escaped punishment from the referee during the game.
Although Chelsea coach Antonio Conte said he did not see the incident, Southampton boss Mark Hughes stated after the game that Alonso should have been given a red card for his challenge, and the governing body agrees with the Welshman.
As a result of his suspension, Alonso will sit out another clash with Southampton as a result, missing Saturday's FA Cup semi-final against them in between Premier League visits to Burnley and Swansea.
A statement from the FA said: "Marcos Alonso will miss Chelsea’s next three matches after an Independent Regulatory Commission ruled he had committed an act of violent conduct against Southampton’s Shane Long.
"Alonso denied the charge and further submitted that if found proven the suspension would be excessive, however, this was rejected following Wednesday's hearing.
"The incident, which was not seen by the match officials but caught on video, occurred in the 43rd minute of Saturday’s game."
Alonso has been a key player for the Blues this term, scoring seven times in 43 appearances in all competitions.
The Blues visit Burnley on Thursday looking to cut the gap between them and Tottenham Hotspur, which currently lies at eight points.