The woman, who is currently on ventilator support at Bharti Hospital and continues to be critical, tested positive for the infection earlier after her throat swabs were sent to the National Institute of Virology to check for the possibility of swine flu (H1N1), a doctor said.
She has no foreign travel history.
All the four people who tested positive for the deadly virus on Sunday are the woman's relatives, districtcollector Naval Kishore Ram told PTI.
They include the woman's son, her sister and the latter's husband and daughter, a health official said.
The woman does not have travel history to a foreign country, but she visited Vashi in neighbouring Navi Mumbai to attend a wedding on March 3.
The district administration on Saturday said a team from the Union Health Ministry has arrived in Pune to check on the woman.
"A team from the Centre arrived in Pune for further probe. We have so far found some 100 people who were in touch with her," Divisional Commissioner Dipak Mhaisekar said.
The total number of coronavirus positive patients in Maharashtra has risen to 74 with 10 more positive cases reported in the last 24 hours, officials said on Sunday.
Of the 10 new cases, 6 are in Mumbai and 4 in Pune, they said.
See Also
Coronavirus cases in India state wise
Coronavirus myths and facts