This would be more than the like the two low recorded in the first quarter of 2009, when Germany was in the midst of the financial crisis, the institutes added.
Germany introduced hypothetical public isolation measures weeks ago, closed schools, shops, restaurants and sports facilities and suspended many production companies to curb the spread of the pandemic.
The economy is likely to shrink by 1.9% between January and March, according to the leading economic research institutes.
Earlier, Reuters quoted sources as saying that Germany's economy is likely to shrink by 4.2 percent this year.
"The Coronavirus pandemic is causing a deep recession in Germany," said the institutes, whose projections form the basis of the government's own economic indications.
The institutes said an unprecedented package of 750 billion euros ($814.73 billion) was approved last month to mitigate the economic effects of the crisis, causing the debt-to-output ratio in Germany to rise to 70 percent this year.
Finance Minister, Olaf Schulz, who pledged to provide an additional stimulus after the pandemic, said Germany's debt could reach 75%.
The institutes added that the unemployment rate in Germany will be 5.9% at its peak.