The woman, who has been identified only by her surname Tian, lives in Shandong Province and welcomed a baby daughter on 25 October.
Her husband Huang Weiping, 68, said the pair had not considered the possibility of being fined.
“We didn’t mean to violate the law. I will put forward an administrative review or initiate a lawsuit if I am fined,” Mr Weiping said, according to Beijing News.
Mr Huang said he believed the couple were exempt from the policy, as regulations only apply to women under the age of 49.
Officials in Shandong Province are reviewing their case. The province’s laws restrict couples to two children each.
Exceptions can be made for people who have children from previous marriages and for the parents of disabled children. Disability remains heavily stigmatised in China.
“The commission will decide whether the fine should be applied after checking information about the couple’s previous two children,” an official told The Global Times, a state-backed Chinese newspaper.
Tian suffered a range of pre-birth complications, including severe pre-eclampsia, heart problems and abnormal liver and kidney function.
Doctors decided to deliver the child through a caesarean section, according to state broadcaster CCTV.
“We were quite lucky, given that the mother was at an advanced maternal age and had a variety of complications,” Liu Wencheng, the doctor in charge of the delivery, said.
The couple also struggled to register the child’s birth because they had lost their marriage certificate.
A government official said the pair had to re-submit forms to finish the registration process.
Mr Weiping and his wife have two adult children in their forties and several grandchildren.
The elder children reportedly disapproved of the birth.
“My daughter even said that if I gave birth to this little baby, she would sever all ties to us,” Tian said, according to CCTV.
Families who violate the two-child policy face fines calculated according to their home city’s average income and the number of children they have.
Fines for breaching the government imposed limit can be debilitating.
Another couple in Shandong, who had a third child in 2017, were fined 64,626 yuan (£7,100) for violating the policy.
After they failed to pay the fee, their entire bank account, containing 22,957 yuan (£2,500) was frozen in February 2019.
Beijing revised its family planning policy in 2016, allowing couples to have two children instead of one.
Additional reporting by agencies
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