It is India's first-ever archery medal in the Paralympics.
Harvinder beat Kim Min Su of South Korea in a close and tight match (6-5) to take India's medal tally to 13.
In the semifinals, the 30-year-old archer lost to world number 10 Kevin Mather of the USA 6-4 in an intense five-setter.
Meanwhile, Prime Minister Narendra Modi congratulated Harvinder for his stunning win at the Paralympics.
"Outstanding performance by Archer Harvinder Singh. He displayed great skill and determination, resulting in his medal victory. Congratulations to him for winning a historic Bronze medal. Proud of him. Wishing him the very best for the times ahead," he tweeted.
Hailing from a middle-class farming family, Singh had dengue when he was just one-and-half years old and a local doctor administered him an injection that had an adverse effect and his legs stopped working properly.