Rajagopal, in 2001, was accused of hiring eight henchman to abduct and murder Prince Santhakumar, according to Indian media.
Santhakumar was married to the daughter of another of Rajagopal's employees and the restaurant chain owner wanted to make her his third wife.
The woman, 20 at the time, refused.
Rajagopal was sentenced to life in prison but was given until July 7 to surrender, on medical grounds.
Saravanaa Bhavan chain - which has been described as the McDonald's of South India - has more than 80 outlets worldwide and employs close to 9000 staff.
Saravanaa Bhavan's Auckland website attributed the growth of the chain to founder "Rajagopal's vision and his keen desire to take his concept worldwide".
But following the Supreme Court decision, the wording on the company website would be changed and the business was distancing itself from Rajagopal.
It plans to open several restaurants in New Zealand, with the next one most likely to be in Queenstown.
Saravanaa Bhavan offers vegetarian dishes on its menu that are exclusive to South India and Tamil Nadu in particular, including rice idli, masala vada, mysore bonda and South Indian thali meals.