Pakistani national Faiza Malik tweeted to Ms Swaraj, seeking her help after the person, who was to donate the organ to his nephew Faraz, was found unfit by doctors at a Fortis hospital here.
Mr Malik said since the person could no longer donate the organ, another man - Faraz Razzaq - from Pakistan be given a visa to travel to India.
"@SushmaSwaraj, Dear madam my nephew Faraz Malik is at Fortis waiting for donor, doctors find previous donor unfit so rejected, please grant visa to Abdul Razzaq CF9864951," Mr Malik tweeted.
Ms Swaraj, responding to the tweet, assured him that the Indian High Commission in Pakistan will give a visa to the second donor. "Please don't worry. I am asking Indian High Commission to give visa for the second donor. @IndiainPakistan," Ms Swaraj tweeted.
Details about the hospital branch where Mr Malik's nephew has been admitted could not be immediately known.
Another Pakistani national, Aamir Xaffar Siddiqi, also sought Ms Swaraj's help stating that his condition was very critical.
"Dear Ms. @SushmaSwaraj, being a heart patient my condition is very critical and it's my humble request to grant us VISA at your earliest convenience. Patient Aamir Xaffar Siddiqi Passport # GV5460871 Attendant Sadia Aamir passport # HD1221521 (sic)," Mr Siddiqi tweeted.
To this, Ms Swaraj tweeted, "@IndiainPakistan will see your papers and report to me."