The war crimes tribunal found Abdul Quader Mollah, assistant secretary general of the outlawed Jamaat-e-Islami party, guilty of murder, rape and torture during the 1971 war of independence from Pakistan.
The life sentence imposed in February also triggered protests by people hoping he would get the death penalty.
In response, parliament amended a law to allow the state to appeal against any verdict or sentence passed by the tribunal. Bangladesh has been hit in recent months by a wave of violent protests over war crimes convictions, presenting the government with a security and credibility challenge ahead of polls early next year. More than 100 people have been killed in protests and counter-protests since January.
Defence attorney Abdur Razzak dismissed the sentence as politically motivated and said it would file a petition for a review, but Attorney General Mahbube Alam said a review was not an option under the constitution.
"This decision over which the accused now has no further right of appeal or review is in clear breach of international law," Mollah's international legal team said in a statement.
"It lends further weight to calls for the war crimes trials to be condemned and replaced by a credible, international criminal tribunal, under the auspices of the UN."
Several Jamaat leaders and two from another group are still on trial at the tribunal. The New York-based Human Rights Watch group has criticised the tribunal's procedures.