The car went on sale on Tuesday with the first deliveries starting in July.
Already dealers are reporting long queues from buyers with the waiting list extending out to 12 months.
The Nano has been designed with low cost in mind.
The budget four-door five-seater car, has a small 22kW 624cc two cylinder engine at the rear and a four-speed manual transmission.
Engineers have trimmed down the car so it appeals to Indians hoping to trade up from a motorcycle.
There is no air conditioning, no electric windows and no power steering, although buyers will be able spend more on those items in two deluxe models, the CX and LX.
The Tata Corporation also intends launching a better-equipped, larger engined Nano in Europe.
Tata is building a new plant in Gujarat in western India to build the car.
It will produce between 250,000 and 500,000 Nanos a year.
The Tata Corporation also owns Jaguar and Land Rover.
It bought the British companies for $US2.3 billion last year.
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