Three-dimensional (3-D) massive multiple-input-and-multiple-output (MIMO) systems, which explore degrees of freedom in both the vertical and the horizontal dimensions, are a promising technology to enhance spectral efficiency in the next-generation communication systems. As an emerging modulation technology with millimetre wave (mm-wave) communication in massive MIMO systems with limited radio-frequency (RF) chains, the spatial scattering modulation (SSM) makes use of beamspace domain resources to further improve the spectral efficiency. However, most published works on the SSM only focus on two-dimensional (2-D) MIMO systems. In this paper, we generalize the SSM system to 3-D space. First, we design a novel generalized 3-D SSM system by considering both vertical and horizontal angles to determine scattering paths, which are selected to convey information bits. Then, we propose a whitening filter based optimal detection algorithm to detect the received symbols with correlated noise, where the correlation is generated by the combination of the received signals from the large-scale planar receiving antenna array. Next, we design a 2-D fast Fourier transform (FFT) based transceiving approach to improve the hardware friendliness. After that, we propose a low-complexity detector based on the linear minimum mean square error (MMSE) detection algorithm. Moreover, we derive the union upper bound on average bit error probability (ABEP) in a closed form and the asymptotic performance expression for the generalized 3-D SSM system. Finally, we analyse the impact of transmission environment on the ABEP performance. Numerical results show that the generalized 3-D SSM system outperforms the conventional 2-D SSM system, which reduces the ABEP by 10× with the same signal-to-noise ratio (SNR) level under the typical indoor environment.