"Presented a hand-woven tapestry from Venkatagiri, Andhra Pradesh woven in Jamdani style to PM Sheikh Hasina," Modi tweeted.
A tapestry is a form of textile art, traditionally woven on a vertical loom.
"Artwork in this tapestry shows Kalpavriksh tree & the Kamadhenu cow," he tweeted.
The Kalpavriksh, or the wish-fulfiling tree, is one of the nine jewels that was churned out of the primal ocean. It is one of the most pervasive motifs in Indian artistic creations.
Modi, who arrived in Dhaka this morning, earlier tweeted, "Hello Bangladesh. I bring with me the affection & goodwill of the people of India."
Modi is on his maiden two-day visit to Bangladesh. Breaking protocol, Prime Minister Hasina received him at the Hazrat Shahjalal International Airport here today.