Suarez is facing a charge of referring to Evra by his "ethnic origin and/or colour and/or race" during the 1-1 draw between the sides in October. If found guilty, he could be banned and/or fined.
The hearing is expected to last two days and an announcement on the outcome is expected by the end of the week.
Evra had told the French TV station Canal Plus that Suarez had used a racist insult to him "at least ten times", but it has been widely reported that the phrase involved was "negrito", which translates as "little black fella" and is regularly used affectionately in South America.
Suarez told Uruguayan media earlier this month: "There is no evidence I said anything racist to him. I said nothing of the sort.
"There were two parts of the discussion - one in Spanish, one in English. I did not insult him. It was just a way of expressing myself. I called him something his team-mates at Manchester call him, and even they were surprised by his reaction."
Liverpool have maintained full support for Suarez in his bid to clear his name.