The 33-year-old was held in Bradford on suspicion of distributing material likely to stir up racial hatred. He has since been bailed pending inquiries.
Featuring children singing in Arabic, the disc shows a dramatisation of a girl vowing to follow in the footsteps of her suicide-bomber mother.
The Yorkshire Post newspaper passed the DVD to police in December.
Stick of dynamite
All three of the DVD's tracks are sung by children in Arabic with English subtitles.
The first sequence, said to describe martyrs in action, shows a woman playing with her two children before leaving home with explosives hidden in her dress.
She is then approached by uniformed soldiers and the camera pauses on her expression before there is an explosion.
After finding out about the suicide on television, her daughter finds a stick of dynamite in her mother's wardrobe.
The girl is seen turning to the camera and speaking while subtitles in English show the words: "My love will not be by words. I will follow my mother's steps."
Suicide bombers
A West Yorkshire Police spokeswoman said: "As part of ongoing inquiries into a DVD that was handed into the counter terrorism unit in Leeds in December, officers arrested a 33-year-old man from Weetwood this morning.
"He has been arrested on suspicion of the distribution of material likely to stir up racial hatred and questioned at a police station in West Yorkshire.
"He has now been bailed pending further inquiries."
Three of the suicide bombers who carried out the 7 July bombings came from West Yorkshire - Mohammad Sidique Khan, from Dewsbury, and Hasib Mir Hussain and Shehzad Tanweer, both from Beeston in Leeds.
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