Parmar was born in India. She had an arranged marriage and came to New Zealand in 1995 with her husband.
She has a degree in biochemistry and a PhD from Auckland University in neurology. She and her husband set up a health products company.
They have two sons and Parmar is a former member of the Families Commission.
In her maiden speech in Parliament she said that while she was proud of her Indian heritage: "New Zealand is the only place I call home."
"I do not consider myself just an ethnic MP. I consider myself an MP who brings many perspectives and experiences along with my ethnicity, which I will apply to the serious and important work of an MP in this House."
According to the 2013 census, 39 per cent of Mt Roskill residents are Asia and just under half of them were born overseas.
National won more Party votes than Labour by a margin of 2188. But it would be an astonishing result if it won the byelection. No sitting Government party in New Zealand has won an opposition-held seat in a byelection.
The Labour candidate is Michael Wood and he will be supported by the Green party as well, which has decided not to field a candidate.