The Court of Appeal said allowing the woman compensation would go against public policy on one's obligations as a parent.
Allowing the woman compensation would go against public policy on one's obligations as a parent, the Court of Appeal said, adding that the expenses incurred in raising the child should not be considered as a loss.
"The duty to maintain one’s child is a duty which lies at the very heart of parenthood, and thus the expenses which are incurred... are not capable of characterisation as a loss," the five-judge appeals court wrote in a 141-page ruling.
In a long-running lawsuit that started in 2012, the woman sued a private hospital, its fertility clinic and two fertility doctors after she was inseminated with the wrong sperm.
According to court documents, it was the second time that the ethnic Chinese Singaporean woman had IVF treatment at the privately-owned clinic. Her German husband is of Caucasian descent.
But she was mistakenly inseminated with the sperm of a complete stranger, an Indian man.
The mistake surfaced only after the child was born and her parents realised she had a different skin tone from her brother.
Worried she might have a genetic problem, the child -- known as Baby P in court proceedings -- was sent for tests which revealed the mix-up.
The hospital admitted to its mistake -- there had been two sets of sperm in the processing area -- and was fined Sg$20,000 ($14,300) in 2011.
The mother sued for damages in 2012 for mental distress as well as pain and suffering relating to the pregnancy, and for upkeep of the child.
This was dismissed by a lower court and upheld by the appeals court on Wednesday.
The judges noted that Baby P was a healthy child who was planned for and that allowing a claim would mean recognising the birth as a mistake.
However, the court also ruled that the woman had suffered a loss of "genetic affinity" with the child and should be awarded damages which come up to 30 percent of the cost of raising Baby P.
"This loss of 'affinity' can also result in social stigma and embarrassment arising out of the misperceptions of others, as was the case here."
The girl, who will be seven this year, is attending an international school in Beijing where the family is now based.