The district court in the southern city of Regensburg convicted Williamson of incitement to hatred on Wednesday after he gave an interview to Swedish television disputing the existence of Nazi gas chambers to kill Jews.
The 72-year-old also said in the 2008 interview that "200,000 to 300,000 Jews perished in Nazi concentration camps."
The prosecution had demanded a higher fine of €6,500 for Williamson, who was not present at the hearing, but the court lowered the amount, as it judged he had no income at present.
Williamson's lawyer argued the conviction should be quashed as the bishop had expected the interview to be aired only in Sweden, where denying the Holocaust is not a crime.
But the actual interview took place in the German city of Regensburg, where it is illegal to deny the Nazis murdered six million Jews during World War II. A previous fine of €6,500 handed down in July 2011 was quashed in February 2012 due to "irremediable procedural problems" in the case. Williamson was expected to appeal the verdict.
While still a member of the breakaway ultra-conservative Catholic fraternity, the Society of Saint Pius X Society, Williamson also hit the headlines in 2009 when Pope Benedict XVI reversed his excommunication in a bid to bridge a rift with the organization.
Benedict later said he would not have made such a move if he had known about Williamson's views on the Holocaust.
Williamson was expelled from the fraternity of traditionalists last year after it said he had disobeyed and disrespected his superiors for several years.