The domestic unit finally settled at 72.74 against the greenback, down 50 paise over its previous closing price.
The rupee weakened for the third straight session on Monday, falling to its lowest level in more than 15 months, after two fresh cases of the coronavirus were detected in the country.
One of the two new cases was detected in the capital, New Delhi, while the other was in Telangana, the government said in a statement taking the total number of people who have tested positive in the country to five.
The epidemic, which originated in the Chinese province of Hubei, has killed 3,000 people worldwide as authorities race to contain infections in Japan, Iran, Italy, South Korea and the United States.
The partially convertible rupee closed the day 0.5 per cent lower at 72.7650 per dollar, its weakest level since November 13, 2018. Over the last three trading sessions, the rupee has shed 1.6 per cent of its value.
Traders said the rupee could weaken further with 73 per dollar level likely to be tested during the week, but expect the central bank to step in and sell dollars to prevent significant losses in the local unit.
The news of the fresh cases pushed domestic shares lower, with the broader Nifty share index falling as much as 1.5 per cent before closing the session down 0.62 per cent.
Earlier in the session, the market rallied as much as 2.1 per cent on hopes that major central banks would take steps to stabilise financial markets amid the virus epidemic.