Hariri was killed by a massive car bomb in Beirut in 2005.
The killing polarised Lebanon and led to the withdrawal of Syrian troops. Hezbollah denies any involvement.
It instead says the assassination was part of an Israeli and US conspiracy.
Shortly before the trial was to start, a bomb blast was reported near a government building in the town of Hermel - a Hezbollah stronghold.
At least two people were killed and several wounded in the attack in the town, which is in the Bekaa Valley, near the northern border with Syria.'No contact'
The BBC's Jim Muir in Beirut says the UN-backed trial is a unique occasion - the first time that a terrorism charge has come before an international court and the first international trials in absentia since the post-World War Two Nuremberg prosecutions.
The bomb attack that killed Hariri and 22 others and wounded 226 more on 14 February 2005 was a seismic event in Lebanese history, fuelling the sectarian divisions between Sunni and Shia Muslims in the country.