In an announcement made today, the commission said it was concerned that selling olive oil and claiming it had healing properties might break relevant regulations and the law.
It also had concerns about the safeguarding of vulnerable people at the London-based charity after one of the charity’s trustees was arrested in 2014.
The commission opened a statutory inquiry on 28 July.
The commission statement did not give further details about the trustee’s arrest, but Gilbert Deya, minister of the church the charity runs, and a trustee, according to the commission website, was arrested in 2014 and charged with raping a female member of his congregation, although he was later cleared.
In January this year, The Sun newspaper claimed Deya was selling £1.99 bottles of Aldi olive oil for £5, claiming it would cure cancer and HIV because he had prayed over it.
The ministry is thought to have a congregation of about 36,000 and has branches in south London, Manchester and Liverpool.
Deya has faced a 10-year battle against extradition to Kenya, having been accused of stealing and smuggling babies from a Nairobi slum hospital, according to The Daily Telegraph.
The commission said it had been trying to address a number of safeguarding concerns with the trustees, but they had "failed to report serious incidents to the commission and to provide adequate responses to the questions raised".
Its investigation will examine trustees’ administration, governance and management of the charity, the charity’s safeguarding policies, procedures and practices, and the circumstances relating to the alleged sale of olive oil as a healing substance.
The commission has also issued a direction ordering trustees to provide responses to the initial questions it posed as part of the investigation.
The charity, which had an income of £866,000 and spent just over £1m in the year to December 2014, and whose objects include advancing Christianity and helping those in need, has been on the charities register since 1996.
Gilbert Deya Ministries did not respond to Third Sector’s request for comment.