We consider the low-Mach-number limit of a compressible two-phase flow model with algebraic pressure closure. We first derive formally the corresponding incompressible non-homogeneous two-phase system: the phase densities become constant, while the volume fractions remain variable and are transported by the flow. We then discuss the rigorous convergence towards this limit. The main difficulty lies in obtaining strong convergence of the partial masses, which is not directly controlled by the standard relative entropy. A logarithmic relative entropy provides the additional control required to close the argument.