Ordering the probe, a bench of Chief Justice Jagdish Singh Khehar and Justice DY Chandrachud said before taking a final call, the court "shall require the presence of the girl".
The bench said it would decide the issue after getting inputs from all, including the NIA, Kerala government and others.
Justice RV Ravindran, a retired judge of the top court, will supervise the investigation.
The order came after Kapil Sibal, appearing for the petitioner, Shafeen Jahan, said the court should decide the issue after speaking to the girl.
Petitioner Jahan has moved the top court challenging the High Court's decision.
Terming the case as "serious" and "sensitive", the court had asked the father of the woman to bring material on record in support of his claims on the alleged marriage of his daughter and that there was a "well-oiled systematic mechanism" for conversion and Islamic radicalisation.
The NIA has recently conducted probes into some cases of 'love jihad,' in which some women were allegedly being sent to Syria to join ISIS.
Jahan, who had married the woman in last December, had moved the top court after the Kerala High Court annulled his marriage saying that it was an insult to independence of women in the country.
The woman, a Hindu, had converted to Islam and later married Jahan.
Senior counsel Indira Jaising told the bench that it was an inter-religious matter and the court ought to be careful in its dealing.
(Inputs from PTI and IANS)