The government said that the woman, who suffered from diabetes and hypertension, as well as her son, had tested positive.
India with its 1.3 billion population and proximity to China has so far come through the global virus crisis relatively unscathed with just 81 reported cases.
However, the number marks a steep increase from only about 30 on Sunday, prompting growing concern.
India announced its first death on Thursday, a 76-year-old man who had died two days previously in the southern state of Karnataka, which has also ordered schools, cinemas and theatres closed.
According to a statement from the government, the deceased woman's son had travelled to Switzerland and Italy in February, and went to hospital in New Delhi on March 7, with a fever and cough.
"As per protocol, the family was screened and since he and his mother had fever and cough, both were admitted," it said in a statement.
"All the precautionary measures as per protocol including screening, quarantine of the contacts is already taken up by the Ministry of Health, Government of Delhi and status is being monitored," it added.
The second death comes as India's suspension of incoming tourists went into effect, and just days after the country ordered the closure of most border points with neighbouring Bangladesh and Myanmar.
On Friday, the Indian Premier League, the world's most lucrative cricket competition, postponed the start of this year's tournament amid mounting anxiety.
Most of the foreign cricketers would not have been able to play in the IPL because of the visa restrictions, however.
Overall, the global death toll from coronavirus has jumped to more than 5,000, as the total number of cases topped 135,000, according to an AFP tally based on official sources.
Postponing the cricket tournament, which draws the world's top players from Australia, England and South Africa, and generates hundreds of millions of dollars in revenues each year, dominated Indian headlines.
But it came as a virtual halt on incoming tourists and business visitors came into effect from Friday.
And the government has also ordered the closing of about half of its 37 land border crossing points with neighbouring Bangladesh, myanmar and Nepal from Saturday.
Halting the IPL came after New Delhi and Mumbai banned large gatherings for sporting events.
Delhi and the southern state of Karnataka have also ordered schools, cinemas and theatres to close.
India also called off its two remaining one-day cricket internationals against a visiting South Africa side. The next game was to be played in Lucknow on Sunday.
The start of the IPL has been put back from March 29 until April 15 "as a precautionary measure" over the coronavirus, the Indian cricket board said.
Media reports said that even if the tournament does start after April 15 it was likely to be without fans in the stadium.
The two-month tournament is a huge revenue earner.
The Twenty20 competition is estimated to generate more than US$11bil for the Indian economy and involves cricket's top international stars like England's Ben Stokes, Australia's David Warner and Indian captain Virat Kohli.
Chinese mobile-maker Vivo paid US$330mil to be the league's top sponsor for 2018-2022.
It involves eight teams playing 60 matches to packed, raucous stadiums of tens of thousands of spectators across India. - AFP
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