"Our family love her and we need her home," Ms Kneeshaw said.
"She is a loving and caring mum of three young children, a daughter and a sister and we miss her dearly."
The family asked the public to look out for Ms Singh and her car, a metallic blue Hyundai Tucson, registration number ENJ73, and to notify Auckland police immediately.
"Please let the police know if you have any other information which could help us to bring Laura home."
Detective Senior Sergeant Paul Newman said initial inquiries with family and friends had not revealed any clues to Ms Singh's whereabouts or her intentions on Monday night.
"There is nothing we have observed thus far that suggests any foul play at Laura's home.
"She was having a text conversation with a friend until just after 8pm on Monday night, but since then there's been no word or sign of her."
Ms Singh's bank accounts had not been accessed and police were not aware that anything is missing from her home, Mr Newman said.
Ms Singh was described as Caucasian, about 160-163cm tall, of thin build and has straight blonde mid-length hair.
"We strongly urge anyone who has information about Laura to contact Auckland City Police on 09 302 6641 or directly on 111," he said.
People could also call Crimestoppers anonymously on 0800 555 111.