Pushp Sharma's report appeared in March in the Milli Gazette, a newspaper aimed at India's Muslim community.
It quoted what was said to be a government document that banned Muslims from travelling abroad to teach yoga for last year's World Yoga Day.
Mr Sharma faces charges of fabricating the document, which he denies.
His report was based on what he said was an official reply from a government ministry that promotes yoga and ayurveda medicine.
The report said that, after several queries to the ministry, it replied saying that none of the 3,841 Muslims who had applied to become yoga teachers had been hired up to October 2015.
A letter printed alongside the article, purporting to be from the ministry, said that 711 Muslims had applied to travel abroad as instructors during the first World Yoga Day last June, but none was selected "as per government policy".
The letter does not include a government letterhead and contains a number of spelling mistakes, including an incorrect spelling of the word "yoga".
The Milli Gazette confirmed Mr Sharma was arrested on Saturday morning. Its editor Zafarul-Islam Khan said the charges were "clear attempts to stifle the freedom of the press".
Police in Delhi told NDTV that Mr Sharma was facing charges of "cheating, forgery and promoting enmity between different groups on grounds of religion or race".
India's Prime Minister Narendra Modi, a yoga enthusiast who says he daily practises the ancient Indian art, lobbied the United Nations to declare 21 June World Yoga Day. The first event was held last year.
His support for yoga, and creation of the new yoga ministry, was criticised as "a campaign to enforce Hindu rituals on all non-Hindus," one Muslim official told Reuters last year.
After opposition from Muslim groups, a series of Hindu practices were dropped from the first World Yoga Day events in India.
In response, a Hindu priest and MP for Mr Modi's BJP party, Yogi Adityanath, said anyone who opposed taking part should "live in a closed room or must jump into the sea".

BHS.com will employ just 84 people, a fraction of the 11,000 who lost their jobs after efforts to find a buyer for the high-street business failed.
The last of BHS's 163 department stores was closed last month.
The new website, which is owned by the Qatari Al Mana Group, will go live in the UK on Thursday.
"We are nimble and efficient, but with a great brand, strong customer base and a proven and dedicated team," said David Anderson, the managing director of the new online operation.
Mr Anderson added that the website would have "a number of advantages over a typical start-up", including an "iconic" brand and a loyal customer base in the UK, including 1.2 million former online shoppers.
BHS.com will sell roughly 75% of the items available on the former online shop, including bedroom, bathroom, cushion and lighting ranges.
The new owner of BHS' online shop, Qatari conglomerate Al Mana Group, already works with a number of high-street brands, such as Zara, Mango, United Colours of Benetton and Reebok.
Mr Anderson said an all-new online technology platform had been developed for BHS, "so we are not inheriting any legacy systems".
He said the majority of people who worked for the previous BHS online operation had been recruited for the new business.

The exercise was carried out in Todmorden, Hebden Bridge, Mytholmroyd, Sowerby Bridge, Elland and Brighouse.
About 2,700 homes were flooded along with more than 4,400 businesses in the area in 2015, said Calderdale Council.
Scenarios played for the exercise included a mock rescue of casualties from a sinking canal boat.
Operation Calderdale16 was its biggest ever live training exercise, the council said.
The Environment Agency has eight flood sirens to warn the upper Calder valley when rivers are expected to flood.
The sirens sounded for about two minutes during the exercise.
Source: Eye on Calderdale
A journalist in India is facing charges over a report he wrote saying Muslims were banned from being yoga teachers under government policy.
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The collapsed retailer BHS is to re-launch as an online shop, selling some of the most popular items previously available on its website.
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Flood sirens have sounded as the "biggest ever" training exercise has been held in parts of West Yorkshire inundated by flooding in December 2015.