The deadline to appoint at least one female director fell at midnight on Tuesday.
However, hundreds of the more than 5,000 companies listed on India's two main stock exchanges have failed to do so.
Mukesh Ambani, India's second-richest man, has appointed his wife Nita to the board of Reliance Industries.
Gautam Singhania named his wife Nawaz as a director of Raymond Group, his textile manufacturing business.
Prime Database, which has compiled figures on the number of companies that had complied with the new law, said some 1,819 companies - about a third - listed on the National Stock Exchange and the Bombay Stock Exchange had still not announced female directors as of Friday last week.
The percentage is believed to have fallen to 17% by the time the deadline fell.
The Securities and Exchange Board of India announced the measure 13 months ago in an attempt to boost gender diversity in boardrooms and had already extended its original deadline from last October.
UK Sinha, its chairman, said last week it was "very shameful" that so few companies already had female directors.
Firms that fail to comply could be penalised by the board.
Shriram Subramanian, head of corporate advisory firm InGovern, said the companies that had not complied were being lazy.
"It is the height of ridiculousness. It is impossible not to find the required number of qualified women from a billion people," he said.
"Firms think if a large number of companies do not follow the norm nobody will be fined and the deadline will be pushed ahead."
Last month, International Monetary Fund boss Christine Lagarde said the lack of female workers in India was a "huge missed opportunity" for the country's economic growth.
India has a population of about 1.2 billion, but ranks 120th for female labour participation among the 131 nations surveyed by International Labour Organization in 2013.
Some of India's richest businessmen have appointed their wives as company directors to comply with a new law.