He was admitted to hospital on 9 February and currently remains in hospital.
Beale founded Line Up almost 30 years ago and has been at the helm of the company ever since.
In his absence, his co-director and business partner Rob Leach will take over as acting managing director.
Rupert Cheswright, Line Up’s head of experiential, will be handling new business enquiries as usual.
Leach said: "Our thoughts are with Duncan and his family, we all wish him a full and speedy recovery."
Line Up has recently been appointed to produce Indesit Company’s week-long product launch in May and events manager Jayson Weston praised Beale in the Power 50 for continuing to "deliver what he promises".
Meanwhile, Compass Group internal communication manager Tim Small told C&IT that "Duncan epitomises trust, reliability and that rare commodity – common sense".