The inquiry into the Al-Hijrah Trust will look into allegations its trustees failed to comply with financial regulations.
The commission, which regulates charities in England and Wales, said it followed an inspection in February.
Lawyers acting on behalf of the Al-Hijrah Trust have declined to comment.
The commission said its inquiry would focus on the charity's finances and particularly the rent it is paid by the Al-Hijrah School.
A spokesman said: "The charity's trustees have repeatedly failed to submit the charity's accounts within the statutory timescales and address concerns, previously raised by the commission, over the charity's internal financial controls."
The commission added the trust was not responsible for the running of the school or its funding, and said the school was not the subject of the inquiry.
In December, Birmingham City Council launched an investigation into claims the Al-Hijrah Trust used Â£1m of taxpayers' money to set up a faith school in Pakistan.
A council spokesperson said: "We continue to work with the relevant statutory agencies and will consider the findings of the Charity Commission."
A charitable trust in Birmingham which runs a school, library, mosque and community centre is being investigated by the Charity Commission.