Emma Pengelly replaced her party colleague Jimmy Spratt as South Belfast MLA on 28 September after he retired.
Mrs Pengelly had previously worked as a special adviser in the Office of the First and deputy First Minister.
She has said she will bring a "great deal of experience" to her new role in that department.
Mrs Pengelly added she was "really enthusiastic about the opportunity".
Earlier this month, a DUP spokesman confirmed Mrs Pengelly would receive a five-figure severance payment from her previous job as First Minister Peter Robinson's special adviser.
Asked about that payment on Tuesday, she said she intended to spend a "considerable amount" on her constituency work.
She said she had neither applied nor asked for the severance payment, and that it would be paid automatically on a statutory basis after she spent almost nine years as a special adviser.
Mrs Pengelly has not yet stood for election but said she was an "incredibly hard worker" and people should judge her on her actions.
The Democratic Unionist Party (DUP)'s newest MLA has been promoted to the post of junior minister exactly a month after taking her assembly seat.