Dhaka Metropolitan Magistrate Mehedi Hasan passed the order after police placed her before the court seeking a seven-day remand in the case filed over Fardin's murder.
Police arrested Amatullah Bushra from her Banasree home in Dhaka on Thursday morning.
Earlier in the day, Kazi Nuruddin Rana, Fardin’s father, filed a case against Bushra and several unidentified people in connection with his son’s death at Rampura Police Station.
Bushra is a 3rd-year student of East West University. Police recovered Fardin's body from the Shitalakhkhya river, behind a cotton mill at Siddhirganj, on November 7, three days after he went missing.
On November 4, Fardin left home and did not return. He was also unreachable on the phone. Later, Fardin’s father lodged a general diary with Rampura Police in this regard.
On Tuesday, Sheikh Farhad, a physician at Narayanganj General Hospital where the autopsy was done, said there were several injury marks on Fardin’s head and body.
Police have detained two friends of Fardin for interrogation, Maniruzzaman Moni, officer-in-charge of Narayanganj River Police, said.
Fardin’s father on Tuesday said that his son was murdered and demanded justice.
"I may not get my son back, but I want justice. It is not difficult to identify the culprits and killers by tracking his mobile phone location," he said after Fardin’s namaz-e-janaza at Buet Central Mosque, on Tuesday.