Roland Molenaar attacked the Turkish mosque in the northern town of Heerenveen on 10 November, just over a week after Van Gogh, an outspoken critic of Islam, was killed as he cycled to work.
His murder sparked a wave of attacks on mosques, religious schools and churches.
The court said the arsonist was motivated by the events of that tense time as well as his extreme right-wing ideas. It also noted that a psychiatrist had concluded that he was suffering from a personality disorder with anti-social tendencies.
"The emotional damage particularly for the Muslim community was great even though the material damage was limited," the Leeuwarden court said in its judgment, adding that six months of the two-year sentence would be suspended.
Dutch news agency ANP said the 25-year-old had called the emergency services after setting fire to the mosque and his voice had been recorded and recognised by police.
A Dutch-Moroccan man with suspected links to a group of radicals has been charged with Van Gogh's murder.