The interior ministry said only half of staff should work and they had to follow precautions such as wearing face masks and observing social distancing.
However shopping malls must remain closed and businesses in coronavirus hotspots will also stay shut.
The move is part of Delhi’s attempt to gradually restart economic activity.
India has nearly 25,000 confirmed cases of the virus and 780 people have died.
Millions of Indian households depend on their local shops for their day-to-day groceries and other essentials.
All shops in rural areas except those in shopping malls were allowed to reopen from Saturday, as are stores in urban areas. However shops in markets are to remain closed.
However officials said alcohol stores had to remain closed and online shopping platforms could only be used to buy essential items