Sex determination tests are banned in India to stop the practice of aborting female foetuses due to a preference for sons.
Khan was not at home when municipal authorities tried to question him about reports that the woman had such a test, Press Trust of India reported.
A complaint filed by an unidentified, non-governmental organisation alleged that Khan and his wife know they are expecting a boy.
Khan has refused to comment.
The 47-year-old actor is popularly known as 'King Khan' in the Indian film industry. He has acted in around 75 Hindi feature films, including many box office hits.
He has also hosted a season of the Hindi version of the game show, Who Wants To Be a Millionaire?
He and his childhood sweetheart Gauri have a son and a daughter.
India's 2011 census showed that the country had 914 girls for every 1 000 boys under age 6, a gender ratio mainly attributed to sex-selective abortions despite the ban on prenatal gender tests.
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