One police source told Reuters news agency that the 10-year-old nephew of chief judge Muhammad al-Uraybi and a third person in the car were also wounded in the attack on Thursday evening.
A second source said the nephew had died and the third person, who was al-Uraybi's sister, was seriously wounded.
It was not immediately clear if the attack was linked to al- Uraybi's work at the Iraqi High Tribunal.
He was appointed chief judge only last week after the government sacked his predecessor for telling Saddam, the former president, he was "not a dictator".
Three defence lawyers working for Saddam and his co-accused have been killed over the past year, and international legal rights groups have questioned whether he can receive a fair trial in the country.
The first police source said the dead man was Kadhim Abdul Hussain, who was in his 40s, and said his son was Karrar.
"They were attacked in Ghazaliya [a largely Sunni neighbourhood] around 7pm yesterday," the source said.
Al-Uraybi has taken a firm line with the defendants in the month-old trial and has ejected Saddam from court in each of the three sessions over which he has presided.
Gunmen frequently attack the relatives of prominent figures because they receive considerably less protection than leading political figures and judges.