We constrain the luminosity and redshift dependence of the intrinsic alignment (IA) of a nearly volume-limited sample of luminous red galaxies selected from the fourth public data release of the Kilo-Degree Survey (KiDS-1000). To measure the shapes of the galaxies, we used two complementary algorithms, finding consistent IA measurements for the overlapping galaxy sample. The global significance of IA detection across our two independent luminous red galaxy samples, with our favoured method of shape estimation, is ∼10.7σ. We find no significant dependence with redshift of the IA signal in the range 0.2 < z < 0.8, nor a dependence with luminosity below L_r ≲ 2.9 � 10¹⁰ h⁻²L_r, ⊙. Above this luminosity, however, we find that the IA signal increases as a power law, although our results are also compatible with linear growth within the current uncertainties. This behaviour motivates the use of a broken power law model when accounting for the luminosity dependence of IA contamination in cosmic shear studies.