Police uncovered the racket last month when they raided the operation's main clinic in Gurgaon outside New Delhi, and had been searching for Kumar ever since.
He was arrested after checking into a hotel in the jungle resort town of Chitwan. Media reports said that Kumar was identified by a hotel employee who recognised him from Indian television broadcasts.
He was found with $230,000 in cash and a checque for $24,000.
Upendra Aryal, a senior police officer in Katmandu, said that police were also investigating whether Kumar was involved in illegal kidney transplants in Nepal.
Officials say the kidney racket spanned at least five Indian states and involved at least four doctors, several hospitals, two dozen nurses and paramedics, as well as a car outfitted as a laboratory.
It was one of the largest transplant rings reported in India for years, and has led to calls for the government to crack down on the trade.
However, Kumar has insisted that the accusations against him are nonsense.
"That is wrong, absolutely wrong. I have not duped anybody," he told dozens of reporters after he was arrested. "I can only say that I have not committed any crime."
Kidney failure has become more common in rich countries, often because of obesity, and a shortage of transplant organs has fuelled a black market that exploits needy donors.