Two dozen cases been detected in three states including 16 in Maharashtra.
The government has said the new variant is “more transmissible” than the original and has urged affected areas to increase testing.
Delta-plus has also been found in the UK and eight other countries - USA, Portugal, Switzerland, Japan, Poland, Nepal, Russia and China.
India’s health ministry says studies showed that Delta-plus - also known as AY.1 - spreads more easily and binds more easily to lung cells.
However virologists have questioned the labelling of the mutated strain as a variant of concern, saying there is as yet no data to show it is more infectious or leads to more serious disease.
“There is no data yet to support the variant of concern claim based on 22 sequences,” said Dr Gagandeep Kang, a virologist and the first Indian woman to be elected Fellow of the Royal Society of London.
India suffered one of the world’s worst wave of Covid infections in April and May, with people dying on the streets due to a collapsed health system and a lack of oxygen supplies. Images of funeral pyres blazing in car parks raised questions over the chaotic vaccine rollout.
On April 26, the country reported 350,000 new cases and over 2,800 deaths in one day.
Daily cases have fallen steadily in recent weeks.
Over the past 24 hours India reported 50,848 new coronavirus infections, health ministry data showed - taking its confirmed case load to just over 30 million.
The official death toll stands at more than 390,000, although the real number is thought to be far higher.
On Monday, India vaccinated a record 8.6 million people as it began offering free shots to all adults, but experts doubted it could maintain that pace.
“This is clearly not sustainable,” Chandrakant Lahariya, an expert in public policy and health systems, told Reuters.
“With such one-day drives, many states have consumed most of their current vaccine stocks, which will affect the vaccination in days to follow.”
With the currently projected vaccine supply for the next few months, the maximum daily achievable rate is four to five million doses, Lahariya added.
The effort has so far covered about 5.5 per cent of the 950 million people eligible - even though India is the world’s largest vaccine producer.
Since May, vaccinations have averaged fewer than three million doses a day, far less than the 10 million health officials say are crucial to protect the millions vulnerable to new surges.
India has been administering AstraZeneca’s vaccine, made locally by the Serum Institute of India, and a homegrown shot named Covaxin made by Bharat Biotech.
Last week, Serum Institute said it planned to increase monthly production to around 100 million doses from July. Bharat now estimates it will make 23 million doses a month.
On Tuesday, TV channel CNBC-TV18 reported that phase-3 data for Covaxin showed an efficacy of 77.8 per cent.
India may also soon have a mass rollout of Russia’s Sputnik V vaccine, and the government expects to import vaccines this year from major makers such as Pfizer.
Although new infections in India have dropped to their lowest in more than three months, experts say vaccinations should be stepped up because of the transmissibility of new variants.