An improvised bomb was exploded before the Dhaka home of Justice Abu Taher Md Saifur Rahman on Thursday evening, police said.
No-one was injured in the blast at Dhanmondi.
Police's Assistant Commissioner Rezaul Islam said several youths on a motorcycle hurled the bomb at Justice Rahman's gate.
Policemen stationed there fired several gunshots but could not detain the perpetrators.
Thursday's blast took place hours after the ancestral home of the other bench member, Justice Quazi Reza-Ul Hoque, was torched in Feni.
On Wednesday, the bench ordered the media blackout on Tarique who had been making controversial comments on Bangladesh's history and the nation's founding father.