In the U.S., the interstate highway system is categorized as a controlled-access or limited-access route, and it is unlawful for pedestrians to enter or cross this type of highway. However, pedestrian-vehicle crashes on the interstate highway system pose a distinctive safety concern. Most of these crashes involve ‘unintended pedestrians’, drivers who come out of their disabled vehicles, or due to the involvement in previous crashes on the interstate. Because these are not ‘typical pedestrians’, a separate investigation is required to better understand the pedestrian crash problem on interstate highways and identify the high-risk scenarios. This study explored 531 KABC (K = Fatal, A = Severe, B = Moderate, C = Complaint) pedestrian injury crashes on Louisiana interstate highways during the 2014–2018 period. Pedestrian injury severity was categorized into two levels: FS (fatal/severe) and IN (moderate/complaint). The random parameter binary logit with heterogeneity in means (RPBL-HM) model was utilized to address the unobserved heterogeneity (i.e., variations in the effect of crash contributing factors across the sample population) in the crash data. Some of the factors were found to increase the likelihood of pedestrian’s FS injury in crashes on interstate highways, including pedestrian impairment, pedestrian action, weekend, driver aged 35–44 years, and spring season. The interaction of ‘pedestrian impairment’ and ‘weekend’ was found significant, suggesting that alcohol-involved pedestrians were more likely to be involved in FS crashes during weekends on the interstate. The obtained results can help the ‘unintended pedestrians’ about the crash scenarios on the interstate and reduce these unexpected incidents.