Media tycoon Mir Quasem Ali, 63, of the Jamaat-e-Islami party, was sentenced to death two years ago.
He had been convicted of offences including murder and torture committed during the war with Pakistan.
The tycoon was hanged at a high-security prison outside Dhaka on Saturday evening.
He was arrested in 2010 and convicted in 2014. He declined to seek a presidential pardon, which would have required an admission of guilt.
