The judge issued her decision Thursday, when the court was closed because of a winter storm. The ruling became public Friday.
A judge in Las Cruces made a similar ruling last month in a separate lawsuit brought by the Las Cruces Sun-News and New Mexico In Depth.
Singleton made her decision after reviewing the audit and determining that it contained confidential information and investigatory methods and could "identify possible witnesses, some of whom may be sources and some of whom may be charged with a crime or accused at a future date."
The audit's executive summary has been released as well as some heavily redacted pages about the general methodology used by auditors.
The open government group wanted Singleton to order the release of portions of the audit that have been withheld.
The group is considering a possible appeal of the ruling, said its treasurer, Greg Williams.
He said in a statement that the foundation was "disappointed with the court's ruling, which permits the attorney general to classify a public document as 'confidential' under the law enforcement exception, even though the document was not created by a law enforcement agency or for law enforcement purposes, and even though the document's conclusion was that no laws had been broken."
Singleton said disclosure of the audit information could hurt the attorney general's investigation and she determined "that it would not be possible to make more limited redactions." She said the attorney general's office is a law enforcement agency and it didn't matter that the auditing firm wasn't.
King, the attorney general, said he was pleased the judge "saw the necessity of confidentiality in the course of our investigation into the allegations."
He said in a statement that "it should be everyone's goal to see that justice is served," including protecting the Medicaid program and ensuring that mental health services are provided to needy New Mexicans.
The department suspended payments to providers in June partly because of the findings of the audit it commissioned from a private consulting group.
Legislators have sharply criticized the administration of Gov. Susana Martinez for failing to give providers an opportunity to review and respond to the fraud allegations before freezing their Medicaid payments. The department has contracted with Arizona companies to take over for some of the suspended providers.