The detainees were kept overnight at a police station in the capital, Dhaka, and were brought to court on Monday, she said.
Dhaka's chief magistrates' court rejected bail for the 19 and ordered them to be detained for a month.
The United News of Bangladesh news agency said that the politicians were picked up from their homes early on Sunday.
Eight of the detainees, including Nazmul Huda, an ex-minister, and Salahuddin Quader Chowdhury, are close aides of Khaleda Zia, the former prime minister, the news agency said.
Those arrested also included two more former ministers and a couple of aides from the Awami League, headed by Zia's predecessor and main rival, Sheikh Hasina.
Feuding between Hasina and Zia over electoral reforms has triggered violent street protests in recent months, and Iajuddin Ahmed, the country's president, imposed a state of emergency on January 11.
National elections had been scheduled for January 22, but were postponed due to the unrest, which has left 34 people dead. No new election date has been set.
The arrests came days after the country's interim leader Fakhruddin Ahmed vowed that his government would crack down on corruption, though it was unclear if Sunday's arrests were related.
The state of emergency bans political activity and gives security forces sweeping powers to detain anyone without a warrant.
Protests erupted in late October when Zia ended her five-year term and handed over power to an interim government to prepare for the parliamentary elections.