The injured were the driver of a van and a 22-year-old woman nearby. Both have been admitted to the trauma centre with gunshot wounds.
Police officer Dinesh Yadav told IANS that the guard slipped while walking towards the bank. His double barrel gun went off after hitting the ground.
Police have booked the guard for carelessness and causing injury.
Spotted: Lara Dutta, Mahesh Bhupathi with their daughter in Bandra
Birthday special: Sushant Singh Rajput's journey from TV to films
Photos: Vibrant Sonakshi Sinha opens LFW 2017 on a cruise ship
Health in pictures: 8 reasons why people have unprotected sex
Photos: 'Peshwa Bajirao' TV show launch event in Mumbai