Spaniard Saiz was shown a straight red card by referee Mike Dean for spitting at Newport winger Robbie Willmott in stoppage time at the end of Leeds' shock 2-1 defeat.
UEFA's rulebook punishes spitting with a mandatory six-game ban and the FA announced Saiz's suspension on their official website, subject to any appeal.
Referee Dean confirmed after the third-round tie that he showed Saiz the red card for spitting and Leeds could now lose the influential Spaniard from their Championship promotion bid until the end of February.
Saiz will be sidelined until the Sky Bet Championship fixture at Derby on February 20 and will miss six league games as Leeds bid to maintain their play-off challenge.
Jonny Evans and Papiss Cisse were both suspended after being found guilty of the offence during a Premier League match between Newcastle and Manchester United in March 2015.
When told of the spitting allegation in the post-match press conference, Leeds manager Thomas Christiansen replied: "If that's right why he got the red card then it's a problem.
"This is something we need to talk about. We need to speak and we'll see what happens."
It is not the first time that Saiz has been involved in a spitting row since joining Leeds from Huesca last summer.
Port Vale manager Michael Brown said Saiz spat at his defender Joe Davis during a Carabao Cup tie in August, but the Football Association did not bring any charges against the 26-year-old.