They were returning from the Amar Ekushey Book Fair at that time.
Doctors declared him dead during an emergency surgery at the Dhaka Medical College and Hospital (DMCH), its police outpost Inspector Mozzamel Haque told bdnews24.com.
DMCH casualty department’s Residential Surgeon Riaz Morshed confirmed to bdnews24.com that Avijit Roy was dead.
Islamist zealots have been threatening Avijit, a bioengineer and a US citizen, for his active campaign against Islamist radicals.
Avijit has been a regular bdnews24.com columnist and the founder of popular blog Mukto-mona.
He is son of well-known physicist Ajay Roy who has taught at Dhaka University for a long time.
Avijit had suffered a deep gash on his head during the assault and Banna lost a finger and suffered cut wounds.
She is still under treatment at DMCH.
Two machetes, a severed finger and a bag that possibly belonged to the assailants were recovered from the scene, Shahbagh police said.
Avijit's blogger friends say he had been possibly trapped – some online bloggers had invited him to a book fair event.
Police are investigating the lead to track down the culprits.
Avijit Roy is well known for his books ‘Biswaser Virus’ (Virus of Faith) and ‘Sunyo theke Mahabiswa’ (From Vacuum to the Great World).
Two of his recent titles had been launched at the ongoing Ekushey Book Fair.
His writing and blogging had evoked the ire of fanatics and he had been regularly threatened.
Thursday’s attack bore a striking resemblance to the one on legendary writer Humayun Azad in February 2004.
Azad was also returning to home from the Ekushey Book Fair when he was hacked with machetes by radical militants. He later died in Germany.
Militants also hacked blogger Ahmed Rajib Haider to death in a similar attack near his home at Dhaka’s Mirpur in February 2013.
That was barely 10 days after the secular platform Ganajagaran Mancha started its Shahbagh-based agitation.
Islamist radicals had attacked other secular bloggers like Ashraful Alam and Asif Mohiuddin after the Shahbagh agitation polarised opinions in Bangladesh.
They were demanding capital punishment for war criminals and a ban on communal parties like the Jamaat-e-Islami.
Farabi Shafiur Rahman was arrested in connection with Rajib Haider’s murder but managed to secure bail later.
He had issued death threats demanding that Rokomari.com, an online shopping portal, stops selling the books of Avijit Roy.