The owner of the courier shop, Vikas Sood, and a customer were injured in the blast which took place on September 26.
The parcel was meant for delivery to Bhupesh Rajyana, Rajyana House, Patiala Gate in Sangrur.
According to the police, the accused was involved in a family dispute with Bhupesh.
Earlier this year, Rajbir Rajjiyana had visited Sangrur to settle the dispute, but failed to resolve the matter, the police said.
Rajbir Rajjiyana was identified with the help of a CCTV footage and subsequently, a police team was sent to Sundergarh district in Odisha to arrest him.
The accused was arrested on October 2, the police said, adding that he was later sent to five days of judicial custody.