Nawaz Sharif has denounced corruption cases against him and his party's leaders as politically motivated, and both brothers deny any wrongdoing.
The younger Sharif was arrested in a "shock" move by the anti-corruption body on Friday when Sharif appeared before it in the Saaf Pani Company case.
Friday's arrest of Shehbaz Sharif by agents of the National Accountability Bureau (NAB) in Lahore involved a case of alleged corruption in a low-priced housing scheme when Sharif was chief minister of Punjab province. He will be kept in a highly-secured lock-up inside the NAB Lahore office until his appearance in court.
He claimed that Shahbaz has been arrested to influence October 14 by-polls.
Stating that PTI is resorting to such tactics as they could not "defeat PML-N in the political arena", Aurangzeb said, "We will not accept revenge in the name of accountability".
Supporters of the PML-N have started gathering outside the bureau's office.
A NAB court on Saturday heard charges that Sharif in 2014 illegally cancelled a contract with a construction company and sought to award it to another company, allegedly for a bribe.
The minister said that these cases were initiated by NAB during the tenure of the PML-N government and then continued.
Shahbaz's son-in-law Ali Imran Yousuf is also facing corruption inquiries in this case.
Lahore Development Authority (LDA) former Director General Ahad Cheema and senior bureaucrat Fawad Hassan Fawad are already in NAB custody in connection with the housing scam.
The PPP chairman said it was unexpected from the government that speaks of justice to arrest the opposition leader. The minister distanced his government from the arrest, saying it is completely "neutral" in this matter, but it will support NAB as "an independent institution" to go after the corrupt.
Reacting to Shahbaz's arrest, the PML-N said that arresting the Leader of the Opposition without seeking the permission of the NA speaker was "against the law". "It appears to be a political victimisation which should be stopped", PML-N spokesperson Marriyum Auranzeb said.
According to sources, Shehbaz Sharif was arrested after Fawad Hasan Fawad, the implementation secretary told NAB that he carried out corruption activities in projects in Punjab on orders from Shehbaz Sharif, who was the chief minister that time. Mr. Nawaz was released from prison last month, pending an appeal against his conviction.
The Panama Papers case is about alleged money laundering by Sharif in the 1990s when he twice served as Pakistan's prime minister to purchase assets in London.