The unnamed official said the attempt against Judge Munir Hadad had taken place on Friday as he was being escorted by a security convoy through Baghdad's western neighbourhood of Ghazaliya.
No one was injured in the attack but some of the vehicles were damaged, he added.
Hadad's exact role on the tribunal that is trying Saddam Hussein and members of his former government, was unclear.
There are about 20 investigative judges and up to 20 prosecutors on the tribunal.
Hadad is not due to participate in the trial, which adjourned on Thursday, until 24 January.
Saddam and his co-defendants are charged with the murder of more than 140 people who were killed in the town of Dujail in 1982 after an attempt on the former leader's life. If convicted, the accused could be condemned to death.