The girls, aged 15 and 16, were studying at the tuition centre in the Basantapur area of the capital when the boy barged into the room and splashed acid on them.
Police said the masked boy fled the scene after the attack, The Himalayan Times reported.
The girls were waiting for their tutor when the incident happened. They were preparing for the secondary school examinations scheduled for next month.
While one of the victims sustained injuries on her chest and a leg, the other girl's face has been disfigured in the attack.
Acid attacks, which disfigure and often blind victims, are a criminal offence in India, there are no specific laws addressing it in Nepal.