The woman, identified as Babli, told media she called Uber after emergency calls to hospitals went unanswered.
The driver of the vehicle told the Times of India that he pulled over because Babli was in excruciating pain.
He then helped deliver the baby with two other women before taking them to hospital.
"He picked me up, put me on a stretcher and dragged it into the hospital," the Times of India quoted Babli as saying.
"I named him after Uber because the baby was born in an Uber cab," she told the Reuters news agency.

The crash has closed the A76 Dumfries to Kilmarnock Road at Sanquhar in south west Scotland.
A major clean-up operation is under way and police say the route is expected to be closed for most of the day.
Lengthy diversions are in operation and motorists are being urged to avoid the area. The driver was not hurt.
The glue container burst when the lorry jack-knifed on the road at 05:30, police said.
The incident happened in the town centre and diversions are in place around the affected area in Sanquhar.
Traffic is able to rejoin the A76 either side of the town but the re-routing has caused difficulties for large, industrial vehicles.
A Dumfries and Galloway police spokesman said: "The glue container on the lorry has burst and glue spilling is affecting the road surface.
"Road diversions are being put in place. However, motorists are asked to avoid the area if possible."
A member of police control staff said the road closure is expected to be in place for several hours.

The 19-year-old, who has yet to make a competitive first-team appearance for the Premier League club, scored eight goals on loan at Poole last season.
Glovers manager Darren Way said: "We feel this next move is a fantastic move for Sam and Yeovil.
"We must thank (Bournemouth manager) Eddie Howe for trusting us with the development of his young talent."
Yeovil begin their League Two season on Saturday with a trip to face Luton Town.
Find all the latest football transfers on our dedicated page.

Kirsty Maxwell, from Livingston, died on Saturday in the tourist area in south east Spain.
It is thought that she was part of a group of more than 30 women who had travelled to the resort for a hen weekend.
A British man was arrested by police in Benidorm in connection with the incident, before being later released.
A Foreign Office spokesman said: "We are supporting the family of a British national who sadly died in Benidorm on 29 April."
He added: "We are in contact with the local authorities following the arrest of a British man."
Mrs Maxwell's body is understood to be found near the swimming pool at the Apartamentos Payma on Saturday.
An Indian woman has named her baby "Uber" after giving birth in a car belonging to the taxi aggregation service.
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A road has been closed after a lorry carrying glue jack-knifed, spilling its load over the carriageway.
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Bournemouth forward Sam Surridge has joined League Two side Yeovil Town on a season-long loan deal.
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A West Lothian woman has died at a holiday apartment block in Benidorm during a hen party.