Friday's blast near the gate of Aun Mohammad Rizvi Imambargah killed eight people and injured 16 others.
The mosque was named after Aun Mohammad Rizvi who was murdered in October 1999 in a sectarian attack. The Imambargah is run by Rizvi's family.
A militant named Hafiz Nawaz was found guilty of Rizvi's killing and awarded the death penalty which was upheld by the Supreme Court in 2011.
Nawaz is a nephew of Riaz Basra, co-founder of the dreaded Lashkar-e-Jhangvi sectarian group. Basra was involved in killings of hundreds of Shias, including Iranian diplomat Sadiq Ganji in 1990.
Regional police chief Akhtar Umar Hayat Laleka said police were exploring links between the Imambargah bombing and the execution of Nawaz, Dawn reported.
"Police will interrogate the convict if necessary. However, a few suspects connected with the bombing are in police custody," he said.