Cala, who joined Cardiff from Sevilla in February, was sent off in the 4-0 loss against Sunderland at the Stadium of Light on April 27, receiving a straight red card and conceding a penalty just before half-time for pulling back Sunderland striker Connor Wickham.
As a result of that sending off, the Spaniard missed the 3-0 defeat at Newcastle United that sealed Cardiff's relegation from the Premier League.
Following an incident near the tunnel at the end of the Sunderland game, Cala was handed a further charge and will now miss Cardiff's final fixture, at home to Chelsea on Sunday, as well as the opening two games of the 2014-15 season.
"Cardiff City's Juan Cala will serve a three-match suspension with immediate effect after a misconduct charge against him was found proven," an official FA statement read.
"The charge, which Cala denied, was that his behaviour in or around the tunnel area after the end of Cardiff's game against Sunderland on April 27 2014 amounted to improper conduct.
"Cala was also fined £12,500 following an Independent Regulatory Commission hearing."
