Mrs Shah has remained in the country on a visitor visa, which expires on February 28.
"The couple chose to withdraw Taraben Shah from the residence application, and were aware of the consequences of their decision," said Michael Carley, Immigration's visa services operations support manager.
He said the health requirements were there to ensure people who were not citizens or residents did not endanger public health or impose costs or demands on the health system.
Mr Carley said Mrs Shah was assessed in 2008 to have severe bilateral knee osteoarthritis with a high probability of needing surgical repair within four years.
Knee replacement costs were estimated at that time to be between $15,000 and $20,000 a knee, he said.
"Disorders such as osteoarthritis with a high probability of arthroplasty are among conditions deemed to impose significant costs and demands on health services," Mr Carley said.
Mrs Shah was also found to have other "significant medical conditions" including reduced hearing, which required a hearing aid, and reduced vision through cataracts that may require surgical repair.
Immigration officer Adam Peterson also said Mrs Shah's "potential contribution to New Zealand was unlikely to be significant".
Son Mukesh Shah, 48, said it was unfair that his parents had to be put in a position where "they have to live apart in their dying years".
"My father has been worried sick and my mother breaks down at the thought of having to return to India alone," said Mr Shah, a permanent resident.
Although the great-grandparents have a daughter in India, Mr Shah said it was "culturally unacceptable" for Indian parents to be living with their daughter, as it was seen as the son's responsibility to provide for them.
Mr Shah, who is a father of two and grandfather to one, said: "It will be a total loss of face for my family and my mother if she was forced to return to India."
He did not think his mother's condition was as bad as Immigration's medical assessors had made out, saying she still led an independent life, and did daily chores such as washing, cleaning and cooking for the family.
"Arthritis, bad hearing and bad eyesight are just common problems that most old people have," Mr Shah said.
"When I suggested they move to New Zealand it was so they can have a better life, and it really pains me to see the move could end up splitting them."
The couple's immigration adviser, Tika Ram, has written to the Office of the Ombudsmen seeking an investigation on whether the decision to deny Mrs Shah a medical waiver was properly made.
He said the department's decision, that could potentially break up the family, was "unfair and wrong".
"Mrs Shah should be granted a medical waiver so that she can remain with her husband and her family here," Mr Ram said.
