His condition is stated to be out of danger.
The arrested suspect is 20-22 years old, he added.
Ahsan Iqbal survived a botched assassination attempt on Sunday during a corner meeting in his constituency in Narowal. He sustained a bullet injury.
In a statement on Sunday night, Labaik leader Khadim Hussain Rizvi condemned the attack on Iqbal and said the party had not authorised any of its supporters to take up arms.
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After the shooting he was rushed first to a local hospital and then airlifted to Lahore, where video footage released by his ruling Pakistan Muslim League-Nawaz (PML-N) showed him being lowered from a helicopter on a stretcher, his eyes open as he responded to questions.
Iqbal, who was shot in the arm Sunday evening during a rally in his constituency Narowal, is now under treatment in Lahore. "We are interrogating him to find out whether he acted alone or at the behest of someone", he said.
Iqbal "was targeted", his aide Asim Khan told AFP, confirming that the attacker has been arrested.
The attacker fired with a 30-bore pistol from a distance of around 18 metres.
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According to the announcement, the Punjab government formed a five-member joint investigation team (JIT), comprising members from the police department as well as intelligence agencies, to conduct an investigation into the attack.
The law's passage had triggered protests by various religious parties, spearheaded by the TLP, who saw the modification to the Khatm-i-Nabuwwat declaration as a severe transgression on Muslims' religious sensibilities.
The shooting comes amid campaigning for parliamentary elections due in July, which have already been thrown into disarray by a Supreme Court decision disqualifying former Prime Minister Nawaz Sharif for his alleged involvement in a wide-ranging corruption scandal.
Iqbal was once seen as a potential prime minister when Nawaz Sharif was ousted by the Supreme Court previous year. "Just spoke to him & he is in high spirits", tweeted Punjab chief minister Shahbaz Sharif, brother to Nawaz.
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Police said the bullet had hit Iqbal in the right arm and gone into his groin.