It comes amid the absence of husband and wife executive principal Dale Burden and deputy principal Yevette Williams from the Cambridge school.
Earlier a spokesman for Worksafe said it had been notified of concerns about staff wellbeing at St Peter's School and was making inquiries.
Shortly after WorkSafe released its statement to the Herald, the school forwarded the Herald an email sent out to parents and caregivers.
In it, chairman of St Peter's Trust Board John Erkkila said the board had begun an independent investigation following a meeting with WorkSafe.
"I want to assure you that the wellbeing of all of our school community – both students and staff – is of the utmost priority to us as a Board, and that the day to day learning continues as normal."
Campus principal Julie Small had addressed students who were "understandably concerned about the speculation surrounding the school", the email said.
Small outlined the importance of being careful about what is said about people and that it is human nature to wonder and speculate when there were question marks over a situation.
"But it's also important that we are mindful of what we say and that we are respectful of people's privacy."
She assured students that their wellbeing was of the utmost importance and their day-to-day activities would not be any different.
School management have also stated that no "student wellbeing matters are involved in the workplace investigation".
It's unclear exactly when Burden and Williams were last at St Peter's School, but it's believed to have been before the end of the first school term.
Parents have been left in the dark over the unexplained absence of the two key staff members.
In an email sent on Monday evening, the school acknowledged queries from parents and caregivers about the two senior staff members but said it was unable to comment further due to privacy reasons.
The Herald's questions were referred to a PR company, which said there was no comment due to privacy reasons.
The school is now in the hands of chief operating officer Rob Campbell who reiterated its stance of being unable to comment when approached again by the Herald.
One parent was supportive of Burden and said the email sent out by the board had only "created more questions than answers".
"The staff and parents that I know have all very much enjoyed working with Dale, and the heads of department that I have become close with.
"He has a big presence at the school and he's very engaging with the students.
"He's a very stand-up guy."
Another parent said he was "shocked and bemused" by the pair's unexplained absence.
"It's an amazing school and the level of communication is amazing, you get a weekly newsletter and so for that [email] to come out on Monday, that was really odd."
The Teaching Council has confirmed it hadn't been notified of any issues about Burden or Williams.
