The scheme, which will be supported by on-air, online and social media activity, is designed to spread awareness for the Owen Wilson and Vince Vaughan comedy, as well as to engage Absolute Radio listeners.
The campaign was negotiated by Robbie Ashcroft, the creative solutions manager at Vizeum UK, and Katherine Knapp, the head of promotions at Absolute Radio.
The winning candidate will work at the heart of Absolute Radio, supporting the production, presenting and music teams, as well as helping with programming, social media and creating multi-platform content.
The scheme follows a similar one put into practice at Absolute Radio in partnership with Orange last year, which featured 650 applications, 250 long-listed candidates and 11 interviewees, before Paul Culliver secured the position. He has since gone on to freelance for the station.
Maria Buttaci, media promotions UK at Twentieth Century Fox, said: "The campaign is very targeted and 'The Internship' mechanic is great because it will not only help to raise awareness for the both the film release and the brand, but it will also give the candidate a fantastic step on the career ladder."
The initial stages of the application process will be entirely anonymous.
Knapp said the promotion was a perfect fit for the station and for Fox: "While driving awareness of the new film, we're offering someone a fantastic opportunity to gain relevant and credible experience at a national radio station."
Absolute Radio and 'The Internship' are also running a separate competition to win Google prizes, including a Nexus 4 phone and a Chromebook computer.