Police's bomb disposal unit defused the first bomb safely at around 10:45pm on Friday.
But the two passersby were injured when splinters went off the second bomb during the deactivation about an hour later, Airport Police Station OC Noor-e-Azam Mia told bdnews24.com.
The Airport Road remained closed for around 10 minutes each in two rounds of bomb disposal.
The two injured people were sent to the hospital, the OC said, but could not identify them.
An airport police officer initially said it was a 'suicide attack', but Dhaka Metropolitan Police ruled it out as an attack of that nature.
He declined to comment on whether militants were involved in the blast, which occurred a week after what the law-enforcing agencies said a suicide attack on a RAB camp in nearby Ashkona.