He is alleged to have removed kidneys from hundreds of poor workers in the northern state of Uttar Pradesh who were lured to his operating theatre.
The collected organs were then allegedly transplanted to wealthy clients, many of whom were from overseas.
Nepali police said Kumar, 40, was carrying more than $200,000 in Indian and foreign currency at the time of his arrest, according to press reports.
Kumar was arrested from a jungle resort in Chitwan, 160km south of Katmandu.
Indian investigators are seeking access to question Kumar in Nepal while Nepalese authorities conduct their own investigation.
Nepalese police are investigating whether Kumar was involved in illegal kidney transplants in Nepal.
A preliminary investigation suggested Kumar was a frequent visitor to the country and had been looking for land where he could build a hospital for kidney transplants.
Indian police have already arrested Kumar's sister-in-law Pooja and her driver Umesh in relation to the racket.
Five other suspects, including another doctor, have also been detained for allegedly luring kidney donors.
His brother, Jeevan Rawat, 36, is still being hunted by police.
Illegal organ transplants are not new in India.
Last year, police in southern India said they found evidence of illegal trade in kidneys sold by poor fishermen and their families whose livelihoods were destroyed by the 2004 Indian Ocean tsunami.