BJP working president J P Nadda said Swaraj was an example of an ideal personality, be as an opposition leader or as external affairs minister.
The country will always remember her as extremely simple, empathic, robust, energetic and impressive personality, Nadda said, adding her death is an irreparable loss to the nation and the BJP.
Describing her as a simple and rare politician, Shah said she was a strong voice of the BJP when it was in opposition and left an indelible mark as a minister.
Defence Minister Rajnath Singh said Swaraj rose through the party's ranks to become the external affairs minister and during her tenure she introduced a new sensitivity and sensibility in the ministry's functioning.
She was known as the people's minister, he noted.
Senior party leader Prakash Javadekar expressed his shock and said Swaraj set an example by connecting the common man's need to the external affairs ministry.
"I have an axe to grind with you Didi . You made Bansuri pick a restaurant to take me for a celebratory lunch. You left without fulfilling your promise to the two of us," Union Minister Smriti Irani tweeted.
Swaraj was brought to AIIMS around 9:30pm and was straight away taken to the emergency ward.
AIIMS doctors said she died of a cardiac arrest. She was 67.
She is survived by her husband Swaraj Kaushal and daughter Bansuri.