Judge Barwiz Muhammad Mahmud al-Marwani and one of his sons were killed on Tuesday in northern Baghdad's al-Adhamyiah district, the official said on Wednesday on condition of anonymity.
Dubai-based satellite TV news network Al-Arabiya reported that the judge and his son died in the attack. The network said the men were killed near their house in northern Baghdad.
Another of the judge's sons, Kikawz Barwiz Muhammad al-Marwani, confirmed his father and brother, lawyer Aryan Barwiz al-Marwani, had been killed.
A tribunal official confirmed the slayings, but said the judge "was not killed because he was working at the tribunal,
"It was something personal. I don't have details, but investigations are still going on," he said.
The judges on the special tribunal had not been identified in public because of concerns for their safety.
Judge al-Marwani was apparently the first one to be killed.
"He was not killed because he was working at the tribunal. It was something personal. I don't have details, but investigations are still going on"
Officials with the interim government could not be reached before dawn on Wednesday for comment.
Al-Marwani's role on the tribunal was unclear, but the law establishing it called for up to 20 investigative judges and up to 20 prosecutors.
It also said the tribunal would have one or more trial chambers, each with five judges.
An official familiar with the court said al-Marwani was an investigative judge.
Set for trial
The killings come one day after five former members of Saddam Hussein's government - including one of his half brothers - were referred to trial for crimes against humanity.
The five referred to trial on Monday included Barzan Ibrahim al-Hasan al-Tikriti, one of Saddam's half brothers, and former vice-president Taha Yasin Ramadan. The three others were senior Baath Party members.
Al-Tikriti (L) is one of five men
referred to trial by the tribunal
The announcement on Monday by the tribunal marked the first time that the special court issued referrals - similar to indictments - which are the final step before trials can start.
Hussein was captured in December 2003, and others have been in custody for nearly two years.
US military officials transferred 12 of the top defendants to Iraqi custody in June with the handover of sovereignty.
They are being held at an undisclosed location near Baghdad International Airport, west of the capital.