The culture ministry said tens of thousands visit the "monument of love" every day and it was "imperative to shut it down".
The Taj Mahal is one of the world's leading tourist attractions, and draws as many as 70,000 people every day.
India has 126 reported cases of Covid-19 and three related deaths. It has tested 6,000 people so far.
On Tuesday, the Indian government announced that all monuments and museums run by the Archaeological Survey of India across the country have also been shut to keep people safe.
Culture Minister Prahlad Patel said all the 143 monuments and museums would remain shut until 31 March and the decision would be reviewed after the shutdown period.
India has taken a number of steps to halt the spread of Covid-19:
All visas, barring a select few categories, have been suspended for a month
Visa-free travel afforded to overseas citizens of the country has been suspended until 15 April and even those allowed in could be subject to 14 days of quarantine
Schools, colleges and movie theatres in most states have been shut until 31 March
The Indian Premier League (IPL), featuring nearly 60 foreign players and scheduled to begin on 29 March, has been postponed to 15 April
India's health ministry says it was among the first countries in the world to prepare for an outbreak of the respiratory illness, and denied allegations that it was slow in testing suspected cases.
Experts say that India is in a critical phase where it needs to halt community transmissions. The country has only tested 6,000 people so far and many believe that it's not enough to halt the spread. Experts say that India needs to start testing thousands daily to effectively stop community transmissions.
The government says it's prepared and has now allowed even private labs to test, apart from government-run labs.