Awais Leghari, another son of the former President, told reporters that his brother was cleaning his gun when it suddenly went off.
Jamal was injured in the left arm and was rushed to Doctors Hospital, where officials said he was out of danger.
Jamal Leghari was elected to the Punjab Assembly in the May 11 polls.
The Leghari family joined the PML-N after three of its members emerged victorious in the elections in Dera Ghazi Khan district, 400 km from Lahore.
