The Federal Office of Public Health said Thursday that the death was reported by authorities in the western canton of Vaud.
The woman had been hospitalized since Tuesday and died during the night.
As of Wednesday afternoon, 58 infections had been confirmed in Switzerland.
Sri Lankan health authorities say they have decided to quarantine all Sri Lankan passengers arriving from Italy, South Korea and Iran for 14 days.
They will be quarantined at a center to be set up at a state-run hospital formally used to treat leprosy patients on the outskirt of the capital, Colombo. Soldiers are now converting the hospital into a quarantine center.
Sri Lanka officially eliminated leprosy in 1995 and the facility was used to keep country's only 16 patients, who will now be transferred to another hospital.
Health Ministry spokesman Viraj Abeysinghe made the announcement Thursday.
More than 104,000 Sri Lankans reside in Italy, with more than 60% in the Lombardy region that has been hit hard by the virus. More than 20,000 Sri Lankans reside in South Korea.
The coronavirus outbreak couldn't have come at a worse time for millions of Hindu revelers who are preparing to celebrate Holi, the festival in which people smear each others faces with colorful powder.
India's Prime Minister Narendra Modi and other top Hindu nationalist leaders are now saying they won't attend any festival celebrations on March 10 in view of the coronavirus outbreak and are advising people to exercise restraint.
Modi tweeted that he would not celebrate Holi as experts have advised to reduce mass gatherings to avoid the spread of the virus.
The message is reaching community leaders who are canceling street celebrations as well large gathering of people in condominiums.
Across India and Nepal and in countries with Indian migrants, Hindus celebrate Holi, the joyous festival of color, smearing one another with red and yellow color powders and spraying each other with squirt guns. Water-filled balloons are also used to color each other.
China says a visit by its president, Xi Jinping, to Japan has been called off because both countries are focusing on combating the virus outbreak.
Foreign ministry spokesman Zhao Lijian says the two sides will be in close communication about a new time for the visit.
"The two countries both agree that President Xi Jinping's state visit to Japan must take place under the most appropriate timing, environment and atmosphere, and must be a complete success," Zhao said at a daily news briefing on Thursday.
The visit had been expected in April.
China has striven to improve ties with Japan as both come under U.S. tariffs meant to punish them for their trade practices. However, mutual suspicion runs high on both sides, driven in China primarily by memories of Japan's brutal occupation of parts of the country last century and China's claim to islands in the East China Sea controlled by Japan.