The convoy was travelling in the Ameen area of eastern Baghdad when the bomb exploded, the official said.
Shadhr, who was kicked out of the secular Iraqiya bloc along with five other MPs last month for refusing to boycott parliament, was not wounded in the blast.
Shadhr and the other five have formed another bloc called Al-Wataniyun (The Nationalists).
Iraqiya began a boycott of parliament and the cabinet in December to protest what it charged was Prime Minister Nuri al-Maliki`s centralisation of power, and it has since called for Maliki to respect a power-sharing deal or quit.
It ended the parliamentary boycott on Tuesday, somewhat easing the political crisis that kicked off as US soldiers departed the country.
Authorities have also issued an arrest warrant for Sunni Vice President Tareq al-Hashemi, an Iraqiya member.
Maliki, a Shiite, has also said his Sunni deputy Saleh al-Mutlak should be sacked after the latter said the premier was "worse than Saddam Hussein".
Hashemi, who denies the charges, has been holed up in the autonomous Kurdish region of northern Iraq and Kurdish officials have so far declined to hand him over to Baghdad. (*)
Editor: Kunto Wibisono
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