52-year-old Narain, the director of Centre for Science and Environment (CSE) and resident of South Delhi's Green Park area, was heading towards Lodhi Garden area on a bicycle when an unidentified car hit her from behind around 6.00 am.
The car driver fled from the accident site.
Ms Narain, was rushed to AIIMS where doctors said that her both arms have been fractured and she suffered grievous injuries in her chest.
"Now her condition is stated to be out of danger but she is still under treatment," said a police official.
The 2005 Padma Shri awardee has also received the World Water Prize for work on rainwater harvesting and for its policy influence in building paradigms for community based water management.
She is also the director of the Society for Environmental Communications and publisher of the fortnightly magazine, Down To Earth.