The charity nevertheless committed to an internal review, saying it wanted to address concerns of members past and present.
More women have since contacted the Herald to share their experiences at Shakti, both positive and negative.
The ministry met with Shakti management on May 12 to let them know about the external review, which will "run parallel" to Shakti's internal review, says Kelvin Moffatt, general manager for service and contracts management at MSD.
He said the issues involve reviewing management and staff employment so it was not appropriate to comment further while the process is underway.
Former Shakti staff and volunteers spoken to by the Herald welcomed the review.
"I would be interested in what this review entails, how they will make sure people who have spoken up are not going to be reprimanded, and if current and former staff will have a safe and confidential process in this review," said a former staff member.
"Shakti and its workers continue to provide an essential service to former refugee and migrant women and their families, and I sincerely hope that the findings from the review enable this work to continue," said another.
Shakti declined to comment on MSD's review.
As a non-profit receiving Government funding, Shakti is separately assessed every two years for accreditation as a social service provider.
At its most recent assessment in September 2019, the charity met nine out of 10 relevant standards, including governance, client-centred services, and financial management.
The staffing standard was "partially met", said MSD general manager for social service accreditation Barry Fisk.
Two "required actions" were issued, related to employment record-keeping and the frequency of board member vetting, he told the Herald.
Required actions need to be addressed but are not critical enough to warrant revocation of the charity's accreditation.
"All required actions were implemented by Shakti to fulfil its obligation to meet the relevant standards in 2019," Shakti said through its lawyer.
The charity is due for its next accreditation assessment in September.