The booking means the Spaniard will miss the Boxing Day match against Bournemouth at Stamford Bridge.
Costa has been in sensational form for Chelsea this season, scoring 12 goals in just 16 Premier League appearances.
“Diego Costa received his fifth yellow card of the season at Crystal Palace”
The 28-year-old has been integral in helping the Blues to the top of the Premier League table after 10 straight wins.
But his booking against Palace will mean Antonio Conte must find a replacement for him against the Cherries.
Michy Batshuayi would be the most obvious option to come in for Costa after making a summer switch from Marseille to Stamford Bridge.
More to follow