The domestic rating agency added that the estimate has a "downward bias", saying predicting the recovery is very difficult at present.
Since the outbreak of the crisis, which has seen the country being put under a 40-day lockdown, watchers have been warning about a heavy toll on the economy, with some analysts also expecting the GDP to contract in 2020-21.
"We are expecting GDP growth to be 1.1-1.2 per cent in FY21 with a downward bias," CARE Ratings said in a note.
The note also said that currently, the agency is not sure when the pandemic will subside or end and what would be the wider ramifications of the same.
However, it said agriculture and government sectors will statistically provide an upward thrust to the economy, which will have many other sectors under pressure.
Mining and quarrying, manufacturing and construction sectors will contract during this financial year, it said adding that financial services, real estate and professional services will have a muted growth of 0.5 per cent.
Demand will be low in the economy and the employment front will be "challenging", it said.
Investment, which has been slow for the past few years, will be subdued as there is surplus capacity and government attention will be more on relief than capital expenditure measures, it said.
The private sector will focus more on completing projects than going in for new ones and the foreign trade will be depressed given recessionary conditions in most countries, the agency said.
It said the restrictions on the movement of non-essential commodities imposed by the states will ensure that the country will not be able to achieve the GST collection target of Rs 1 lakh per month. AA HRS