The men, who are 66 years and 46 years old, are currently under observation, a government spokesperson said.
These are the first cases of the new Omicron variant to be reported in India.
The World Health Organization (WHO) has warned that Omicron poses a "high infection risk"
Officials said all primary contacts and secondary contacts of the two men have been traced and are being tested as well.
Six samples from people who tested positive for Covid-19 in the national capital Delhi, and another six samples from the western state of Maharashtra, have all been sent for genome sequencing to determine the variant. Officials are still awaiting results. Several other cities and states are following suit.
Starting Wednesday, India announced new travel restrictions for international passengers arriving from "at risk" countries a list that includes UK, South Africa, New Zealand, Bangladesh, Hong Kong and Israel.
They will be tested on arrival and cannot leave the airport without their test results. Those who test positive will be isolated and treated, and their samples will be sent for genome sequencing. Those who test negative must quarantine at home for seven days and get tested again on the eighth day.
Different Indian states have announced different policies for travellers - all passengers flying in to Maharashtra from "at-risk" countries will have to spend seven days in institutional quarantine. Delhi and Karnataka have said all international passengers will have to undergo PCR tests on arrival.
"We are immediately checking suspicious cases and conducting genome sequencing," health minister Mansukh Mandaviya told Parliament on Tuesday.
"We have learnt a lot during the Covid crisis. Today, we have a lot of resources and laboratories. We can manage any situation," he added.
Last week, Prime Minister Narendra Modi reviewed the country's public health preparedness, and urged people to continue following Covid safety norms.
Life in India India has returned to normalcy in the wake of low case counts and a steady vaccine drive.
The country has been recording fewer than 10,000 new cases daily and has vaccinated nearly 80% of the 940 million eligible adults with at least one dose so far.
But the latter has begun to slow and the emergence of a new possibly more infectious variant has raised the spectre of a third wave - a frightening prospect given how the second wave devastated India in April and May as hospitals ran out of beds, oxygen and medicines.
South Africa alerted the world to the new variant on 24 November after it detected its first case of Omicron. Several countries have since announced travel restrictions.
Initial evidence suggests Omicron has a higher re-infection risk. But scientists say it will take another three weeks to know how the heavily mutated variant impacts the effectiveness of various vaccines. (CNN)