In this second paper of the series, we focus on the X-ray properties of the OB star population of NGC 6231. As a tool for our analysis, we performed a literature-based census of the OB stars in the field of view. More than one hundred objects are found, among which 30% can be associated with an X-ray source. All the O-type stars are detected in the X-ray domain as soft and reasonably strong emitters. [...] Among B-type stars, the detection rate is only about 25% in the sub-type range B0-B4 and remains mostly uniform throughout the different sub-populations while it drops significantly at later sub-types. The associated X-ray spectra are harder than those of O-type stars. Our analysis points towards the emission being rather associated with a physical (in a multiple system) PMS companion. However, we still observe a correlation between the bolometric luminosity of the B stars and the measured X-ray luminosity. [...]