Swaraj's intervention came after the infant's father brought the matter to her notice on Twitter.
Earlier this week, Ken Sid, a Pakistani national, reached out to Swaraj through the social media platform for a medical visa for his son, who has a heart complication which cannot be treated in Pakistan.
"The child will not suffer. Please contact Indian High Commission in Pakistan. We will give the medical visa," she had said.
The family had been trying to get a visa for three months.
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Ailing Pakistanis frequently to travel to India on medical visas to seek treatment for complicated health problems.
Indian hospitals have previously reported receiving around 500 patients from Pakistan every month. Many of the unwell needed a liver transplant, which costs between Rs2-3 million.
In 2015, five-year-old Basma from Pakistan had been granted a visa to India for an emergency liver transplant surgery. There are now many tales like hers, sometimes with footnotes on how the travelling patients were helped financially by Indians.
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