The move follows a legal complaint lodged by a Croat association in France over a 2012 interview Bob Dylan gave to Rolling Stone magazine.
In the interview Bob Dylan allegedly compared the relationship between Jews and Nazis to that of Serbs and Croats.
Bob Dylan, 72, was served notice of the investigation last month.
At the time the singer was in Paris to receive the Legion of Honor, a prestigious French award.
In the Rolling Stone interview, Bob Dylan was sharing his thoughts about US history and the country’s racial divide.
The singer is reported to have said: “Blacks know that some whites didn’t want to give up slavery – that if they had their way, they would still be under the yoke, and they can’t pretend they don’t know that.
“If you got a slave master or [Ku Klux] Klan in your blood, blacks can sense that. That stuff lingers to this day. Just like Jews can sense Nazi blood and the Serbs can sense Croatian blood.”
During WWII, the Croat Ustashe fascist movement killed hundreds of thousands of Serbs, Jews, Roma and others in their death camps.
Croats and Serbs also fought each other during the break-up of Yugoslavia, in a 1991-1995 war that left around 20,000 people dead.
After the interview was published, the Council of Croats in France (CRICCF) filed a complaint.
Being placed under judicial investigation means that authorities are taking the complaint seriously, but that it won’t necessarily go further.
Bob Dylan, who played concerts in Serbia and Croatia in 2010, rose to fame in the 1960s partly for his support of the US civil rights movement.
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