Police, however, say they know nothing about the detention of the fourth son of Azam, who had been convicted and sentenced to 90 years in prison for 1971 war crimes.
The Jamaat supremo died while serving his sentence.
Dismissed Bangladesh Army Brigadier Amaan Azmi's brother Salman Azmi, who lives in the UK, told bdnews24.com by telephone that several men, identifying themselves from the Detective Branch, took his brother away from his Dhaka home on Monday.
Amaan's brother Salman said, "Our family are yet to decide about filing a GD (general diary). He was the only one among the brothers in Bangladesh. And we doubt that police will cooperate with us."
Amaan, sacked from the army in 2009, is the fourth among six brothers. His brothers live in the UK.
In 2015, he kicked up a social media storm by raising doubts about the number of 1971 martyrs.
In a statement on Tuesday, the Jamaat-e-Islami demanded Amaan's release and described him as a 'non-political person in retirement.'
"He is a law abiding citizen and his arrest is illogical as well as illegitimate," it reads.