BCC Acting CEO Imtiaz Mahmud Jewel filed a general diary with Kotwali Model Police Station in the city on Sunday after he received the message on Thursday last.
"Be careful, the time of your existence is set under our sharp sword. ABT," the SMS sent from the number 01629967551 read, according to Imtiaz.
He said the number is switched off since the SMS is received.
Kotwali Model Police Station SI Asadur Rahman said police were looking into the matter.