Sunanda Pushkar’s body was found in a Delhi hotel room on Friday.
On Tuesday, doctors said she may have died from an overdose of drugs.
Magistrate Alok Sharma directed police to investigate whether the overdose was deliberate or accidental.
Shashi Tharoor and Sunanda Pushkar became embroiled in a row last week after Twitter messages suggested he was having an affair with Pakistani journalist Mehr Tarar.
Magistrate Alok Sharma told the Indo-Asian News Service news agency that he had ordered the inquiry into Sunanda Pushkar’s death after going through the findings of the autopsy report.
“The post-mortem report reveals that she died due to [drug] poison. But it will be too early to say before her viscera report if she had consumed poison, or the drug consumed by her acted as poison,” Alok Sharma said.
Alok Sharma declined to reveal the full findings of the autopsy, but doctors have said that the “preliminary report shows there was drug overdose”.
The autopsy also found “injury marks” on Sunanda Pushkar’s body, but did not say if they were linked to her death.
Meanwhile, Sunanda Pushkar’s son said his mother “was too strong to commit suicide”.
In a press statement released on Tuesday, Shiv Menon said media reports on his mother’s death were “untrue and outrageous” and defended Shashi Tharoor.
“I also do not believe that Shashi was capable of physically harming her, let alone the speculation that he could have taken her life. They were very much in love, despite occasional differences, which they always overcame,” Shiv Menon said.
A public row broke out last week when seemingly private messages between Shashi Tharoor and Mehr Tarar were published on his Twitter feed.
Sunanda Pushkar, 52, said she had gone into her husband’s account and published the messages, accusing Mehr Tarar of stalking her husband – an allegation denied by the Pakistani journalist.
Shashi Tharoor and Sunanda Pushkar later insisted they were happily married and blamed “unauthorized tweets” for causing confusion.
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