The 24-year-old was punished in the aftermath of Cardiff's demoralising 4-0 defeat at Sunderland last weekend, that loss leaving the Welsh club rooted to the bottom of the Premier League and two points adrift of safety.
Cala - who joined Ole Gunnar Solskjaer's squad from Sevilla in February - received a straight red card and conceded a penalty for pulling back Sunderland striker Connor Wickham.
The FA subsequently charged the Spaniard for an incident near the tunnel after the game, with Cardiff announcing on Friday that he wants a personal hearing.
"Juan Cala has requested a personal hearing with the FA in relation to his FA misconduct charge, the date to be confirmed," the club posted on their official Twitter account.
Cala's dismissal will see him miss Cardiff's crucial last two fixtures of the season.
Cardiff will be relegated from the Premier League if they fail to beat Newcastle United on Saturday and at least one of Norwich City, Sunderland or Fulham win.
