The western state of Rajasthan reported the most number of omicron cases with nine, followed by eight in Maharashtra, two in Karnataka and one each in Gujarat and the capital New Delhi.
"The people of Delhi must get fully vaccinated, wear a mask and maintain social distancing," its health minister Satyendar Jain said on Twitter.
He said the city's first omicron patient was being treated at a state-run hospital. Some 94% of its adults had received at least one dose, he added.
The country has fully vaccinated 51% of its 944 million adults and given at least one dose to 85%. Tens of millions of people, however, are overdue for their second dose despite ample vaccine supplies, government data shows.
India reported its first two omicron cases in the southern state of Karnataka on Thursday, in one person with no recent travel history.
Most other cases have been in people who have recently come from abroad, but doctors said the mutated virus was already spreading in the local population as well.
"Omicron is here, community spread is underway," surgeon Arvinder Singh Soin, who has been treating COVID-19 patients, said on Twitter. "Mask up. Get FULLY vaccinated."
India reported 8,895 new COVID-19 cases for the past 24 hours, taking the total to 34.64 million. Deaths rose by 211 to 473,537.
Since a record surge in infections and deaths in April and May due to the delta variant, new cases have hovered around 10,000 in the past few weeks.