The incident occurred at Monirampur village in western Bangladesh when a mob of 3,000 people made a vain attempt to block police from arresting four activists of the Jamaat-e-Islami party, officials said.
The latest killing brought the death toll from clashes stemming from the trials to 89 since January 21 when the war crimes court handed down the first of its verdicts in cases dating back to the 1971 war.
The demonstrators "attacked our car in a bid to snatch the detainees", local police chief Ali Azam told AFP.
Police at first opened fire using rubber bullets and tear gas to disperse the mob but "our lives were at stake and we were forced to open fire", he told AFP.
"One bullet hit a Jamaat man who died on the way to hospital," he said.
For months, Jamaat has been staging nationwide strikes and violent demonstrations to protest against the war crimes trial which has placed nearly the entire party leadership in the dock.
The special tribunal is hearing cases of people accused of committing atrocities during Bangladesh's 1971 war.
Two of the party's leaders have already been convicted by the tribunal, including a vice-president sentenced to death last month. Two leaders of the main opposition Bangladesh Nationalist Party (BNP) are also standing trial.
Both Jamaat and the BNP have charged that the trials are based on trumped-up charges and are more about the government seeking to settle political scores with the opposition than delivering justice in the Muslim-majority nation.
But the government says the trials are needed to heal the wounds of the 1971 war in which it says three million people were killed and 200,000 women raped. Independent estimates put the death toll between 300,000 and 500,000.
Analysts say the trial has plunged the impoverished country into one of its most turbulent chapters and threatens lasting damage to fabric of the world's eighth-most populous country.
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Very Good news! One Fundo less from the world
@"Analysts say the trial has plunged the impoverished country into one of its most turbulent chapters and threatens lasting damage to fabric of the world’s eighth-most populous country." . But the liberals and Indians are so happy...
Biased & one sided reporting.. legacy of ET