We show that the κ-deformed Poincaré quantum algebra proposed for particle physics has the structure of a Hopf algebra bicrossproduct U(so (1, 3)) ?T . The algebra is a semidirect product of the classical Lorentz group so(1,3) acting in a formed way on the momentum sector T. The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the κ-Poincare acts covariantly on a κ-Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics.