He was charged with extorting $147,000 from a construction company, Mahbub Morshed, the police investigator said.
Tarique, a senior leader of Zia's Bangladesh Nationalist Party, denied the allegations.
On Monday, police investigators urged the court to remand Tarique into custody to allow them more time to investigate, Morshed said.
Bangladesh's military-backed interim government has launched an anti-graft drive since President Iajuddin Ahmed declared a state of emergency on January 11.
Dozens of politicians, including former ministers, have already been detained on corruption charges.
A second bail petition by Tarique is due to be heard on March 19, court officials said.
If convicted, he could face a jail term of up to five years as well as a fine, according to lawyers.
Zia joined politics after her husband, President Ziaur Rahman, was slain in a 1981 military coup.
She ended her five-year term in October and handed over power to an interim government to prepare for parliamentary elections.
Tarique has been widely seen as a potential successor to his mother for the job of prime minister.