Mandragora is caught on television cameras shouting "Porca Madonna - Dio Cane", which translates in English to an insult to the Virgin Mary, while also referring to God as a "dog".
He has subsequently been banned for the upcoming fixture against Fiorentina after Lega Serie A confirmed it had been sent an email regarding the player's behaviour.
In Italy, blaspheming is regarded as one of the worst types of swearing, and the Italian FA subsequently treat all such cases with a hard-line policy.
As the referee did not see it, the federation reviewed the footage, and found "he used blasphemous expressions in the 48th minute".
Radja Nainggolan also found himself in trouble earlier this year, as he posted a video on Instagram of him swearing, drinking and smoking over New Year.
"I am very sorry for what happened last night," he wrote. "As you all know, I like to have fun with friends and love to celebrate New Year.
"But last night I went too far: I saw it as a special night, where it is OK to be a little more excessive, but of course I did not want to set a negative example.
"For this reason, I feel the need to apologise for my words and my behaviour."
Mandragora joined Udinese this summer and has made three appearances for the club.
He has also won one cap for Italy, playing 90 minutes in a 3-1 friendly defeat to France.