Sources told Reuters last year that the Seattle-based company was planning to enter the highly competitive business in India, but the move was delayed as the company tried to sort out logistical issues.
Amazon launched its Prime services in India in 2016 and already offers services such as video and music streaming as well as grocery delivery in many cities across the country.
The company's move comes at a time when both Swiggy and Zomato struggle in the face of the COVID-19 pandemic, which has forced the two startups to cut jobs and keep a tight lid on costs.
Indians went into the world's biggest lockdown two months ago as the government tried to curb the spread of the virus, banning social gatherings and shuttering most restaurants and pubs.
Meanwhile, Ant Financial-backed Zomato, which bought Uber's loss-making food delivery business earlier this year, and Naspers-backed Swiggy said they would begin delivering alcohol in some cities starting Thursday.