The accident happened when the family on a scooty was passing through the site of Metro construction near HBR Layout on Tuesday.
The deceased have been identified as 25-year-old Tejaswini and two-and-half-year-old son Vihan.
According to police, Lohit Kumar, a civil engineer, was dropping his wife Tejaswini to her work and sons to a child care centre.
Lohit Kumar and another son escaped miraculously with minor injuries.
Tejaswini and Vihan suffered major head injuries and succumbed to injuries due to severe bleeding. Tejaswini hailed from Dharwad.
Chief Minister Basavaraj Bommai reacting to the incident stated that he would get all information regarding the construction work by the Bengaluru Metro Rail Corporation Limited (BMRCL). The police have taken up further investigation.
IANS