He made the remarks after a meeting with the Asian Development Bank's Country Director Manmohan Parkash at the Secretariat on Monday.
Papia was arrested alongside her husband Sumon Chowdhury alias Moti Sumon and their two associates, Sheikh Tayeba Noor and Sabbir Khandaker, were arrested at Shahjalal International Airport in Dhaka on Feb 22.
They are accused of making a fortune through “trading in drugs and arms, extortion, recruitment fraud and other sorts of embezzlement”. Papia is also believed to be involved in sex trade at luxurious hotel suites.
Jubo Mohila League, an associate body of the ruling Awami League for young women, subsequently expelled Papia as its Narsingdi unit general secretary for breaching organisational discipline.
"The criminal will be punished in accordance with the law. This government hasn't allowed anyone to get away with crimes, irrespective of their political affiliation. All criminals will be brought to justice. Papia too will face justice as a criminal regardless of her political identity," said Road Transport and Bridges Minister Quader.
"There's no reason to think that they won't come forward. Everything will come up when the matter reaches court."
According to Quader, the situation with Papia would not have arisen had the government been aware of her involvement in crimes.
When a journalist asked whether the arrest of Papia was part of the government crackdown on wrongdoings, he said the law enforcement and judiciary were free to arrest and punish anyone involved in crimes.
“Have you seen ruling party criminals facing justice during any previous government?” Quader asked.