Those granted visas included a 14-year-old girl requiring an open heart surgery.
"We have approved visa for the open heart surgery of your sister Huma Usman. She is just 14 years old. We pray for her good health and long life," Ms Swaraj tweeted to Ms Huma's brother.
Last week, Pakistan had accused India of "politicising" a humanitarian issue, but notwithstanding the allegations, Ms Swaraj has been announcing granting of travel permission to Pakistani citizens.
The external affairs minister has also assured issuance of visas to four other Pakistani nationals, including a five- year old girl, considering seriousness of their medical conditions.
"I am sorry, the child is suffering so much. We will issue the visa immediately," Ms Swaraj tweeted, in response to request for medical visa to the girl, Nabeha Rashid, who also requires an open heart surgery.
On Twitter, Ms Swaraj today announced granting visas to Huma Usman, Tariq Hussain, Mubarak Ali and Sakina Yunis. Touched by Ms Swaraj's gesture, those who were granted visas and many of their relatives heaped praise on the minister.
"We are thankful to you and your country for whole life because of your support," said Shahnawaz Qasmi, brother of Tariq Hussain, adding allowing him treatment in India is like giving him a "new life".
Ms Swaraj has been adopting a humanitarian approach in granting visa to Pakistani nationals on medical grounds even as ties between the two countries have nosedived over a host of sticky issues, including cross-border terrorism.
Addressing a regular briefing on Thursday, Pakistan's foreign ministry spokesperson Mohammad Faisal had said the Indian policy of selective issuance of medical visas to Pakistani citizens was "regrettable".