A Tamil source said Wigneswaran rejected the invitation because he did not want to promote tokenism.
President Rajapaksa, who has confirmed his participation in the swearing-in ceremony in New Delhi on Monday, had invited Wigneswaran to be part of his entourage.
Wigneswaran had said he would consult the northern provincial council on Rajapaksa's invitation.
Modi will be administered the oath as 15th Prime Minister of India by President Pranab Mukherjee at a ceremony to be attended by over 3,000 guests.