Pintu told bdnews24.com that he filed a General Diary at Adabor Police Station on Wednesday after he saw the threat in his Facebook inbox.
"I don’t regularly access my Facebook account. This threat message was sent on Jun 3 but I saw it yesterday and lodged a police complaint," he said.
"Free thinker, your turn is next. We will hack you to death," said the message on Pintu's inbox.
The death threat message is a mix of Romanised Urdu and Bangla and it has baffled Pintu.
"I am not a blogger, I don’t write about religion, so why me?" Pintu told bdnews24.com.
Adabor police OC Shahinur Rahman said security has been beefed up in Pintu's house after the complaint about the threat.
But the artist is not cowed down by the threat.
His Facebook posting dares anyone trying to kill him.
"I am not a banana tree. I am the son of a freedom fighter and we know how to fight," he said in a post.
"Before you come to kill me, take leave of your mother because you will not go back," said Pintu, who has designed thousands of book covers so far.