Canadian police charged the three on Friday over the murder of Sikh separatist leader Hardeep Singh Nijjar and said they were probing whether the suspects had links to the Indian government.
Jaishankar said he had seen news of the arrests and said the suspects "apparently are Indians of some kind of gang background ... we'll have to wait for the police to tell us".
"But, as I said, one of our concerns which we have been telling them is that, you know, they have allowed organised crime from India, specifically from Punjab, to operate in Canada," Jaishankar said.
Sanjay Verma, India's high commissioner to Canada, said that it hopes to get regular updates from Canadian authorities regarding the three arrested Indians.
"I understand that the arrests have been made as a result of investigations conducted by the relevant Canadian law enforcement agencies. This issue is internal to Canada and therefore we have no comments to offer in this regard," Verma said.
The trio, all Indian citizens, were arrested in the city of Edmonton in Alberta on Friday, police said.
Nijjar, 45, was shot dead in June outside a Sikh temple in Surrey, a Vancouver suburb with a large Sikh population.
A few months later, Canadian Prime Minister Justin Trudeau cited credible allegations of Indian government involvement, prompting a diplomatic crisis with officials in New Delhi.
Nijjar was a Canadian citizen campaigning for the creation of Khalistan, an independent Sikh homeland carved out of India.
The presence of Sikh separatist groups in Canada has long frustrated India, which had labelled Nijjar a "terrorist".
Canadian police said they had worked with US law enforcement agencies, without giving additional details, and suggested more detentions might be coming.
