Metricon has had at least 60 complaints lodged against it with NSW Fair Trading since March, according to the agency's online complaints register.
Some complaints had been proven by the agency.
"I'm concerned about it," the NSW premier told reporters on Friday.
"They've been the subject of six complaints ... that have been upheld by Fair Trading since 2019," Mr Minns said.
"If action is to be taken by Fair Trading, that's exactly what will happen to protect consumers and those that purchase property in NSW."
Some complaints against the builder relate to service quality, work and contracts, the ABC reported.
But a Metricon spokesperson told AAP it had not been contacted by NSW Fair Trading regarding any inquiries.
"We are open to any discussions that can lead to resolving any concerns," the spokesperson said.
"We have always been committed to providing assistance whenever needed and are ready to help."
The company said it had completed 2144 homes in NSW in the past four years and "remained steadfast in our commitment to delivering excellence in every home we build".
Starting about 6000 home builds a year across Victoria, Queensland, NSW and South Australia, Metricon has ranked first among all residential builders for the past seven financial years.
NSW Fair Trading was not immediately available to confirm if a probe was underway.
The claims against Metricon come amid troubles in the sector including the high-profile collapse of builder Porter Davis, which fell over in March carrying about $147 million debt.
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