Five handmade bombs exploded near the Baitul Mokarram National Mosque ahead of the arrival of Azam's body at the mosque for funeral prayer, but no casualty was reported, police said.
"The janaza of a war criminal can never be held at the national mosque," Ziaul Hasan, chairman of Bangladesh Sommilito Islami Jote, an alliance of progressive Islamic parties, said at a human chain near the mosque.
92-year-old Azam, who was sentenced to 90 years in jail for masterminding atrocities during the 1971 independence war against Pakistan, died on Thursday at Bangabandhu Sheikh Mujib Medical University hospital in the capital Dhaka after suffering a stroke.
He was buried at the family graveyard in the capital. He was kept at the hospital's prison cell since his arrest three years ago for 1971 war crimes. He was suffering from old age ailments including heart and kidney disorders.
Last year Azam, the ideological linchpin of Jamaat, was sentenced to 90 years in jail after being found guilty of charges relating to 1971 war of independence with Pakistan.
Azam, who has left deep emotional scars in the collective national psyche by engineering war-time atrocities in 1971, was found guilty of all five categories of crime - conspiracy, planning, incitement, complicity and murder.
His conviction sparked deadly protests by Jamaat and widespread celebration amongst secular groups. Azam, however, declined to have committed any crime in 1971 and refused to regret.
Meanwhile, Jamaat-e-Islami in Pakistan also held funeral prayers in different parts of the country, mourning the death of Azam, local media reported.