It is the sixth blast to hit Beirut and the surrounding area in the past four weeks. Two people have been killed in the five previous explosions, all caused by bombs.
Walid Eido is a Sunni Muslim member of the Lebanese Future Movement (Saad al-Hariri's party), which is part of the March 14 majority bloc.
Eido was a retired judge, who had been critical of Hezbollah and Emile Lahoud, the president, who recently called on Fouad Siniora, the prime minister, to launch an investigation into last year's war.