Vision standards for driving are typically based on visual acuity, despite evidence that it is a poor predictor of driving safety and performance. However, visual motion perception is potentially relevant for driving, as the vehicle and surroundings are in motion. This study explored whether tests of central and mid-peripheral motion perception better predict performance on a hazard perception test (HPT), which is related to driving performance and crash risk, than visual acuity. Additionally, we explored whether age influences these associations, as healthy ageing impairs performance on some motion sensitivity tests. Sixty-five visually healthy drivers (35 younger, mean age: 25.5; SD 4.3 years; 30 older adults, mean age: 71.0; SD 5.4 years) underwent a computer-based HPT, plus four different motion sensitivity tests both centrally and at 15° eccentricity. Motion tests included minimum displacement to identify motion direction (Dmin ), contrast detection threshold for a drifting Gabor (motion contrast), coherence threshold for a translational global motion stimulus and direction discrimination for a biological motion stimulus in the presence of noise. Overall, HPT reaction times were not significantly different between age groups (p = 0.40) nor were maximum HPT reaction times (p = 0.34). HPT response time was associated with motion contrast and Dmin centrally (r = 0.30, p = 0.02 and r = 0.28, p = 0.02, respectively) and with Dmin peripherally (r = 0.34, p = 0.005); these associations were not affected by age group. There was no significant association between binocular visual acuity and HPT response times (r = 0.02, p = 0.29). Some measures of motion sensitivity in central and mid-peripheral vision were associated with HPT response times, whereas binocular visual acuity was not. Peripheral testing did not show an advantage over central testing for visually healthy older drivers. Our findings add to the growing body of evidence that the ability to detect small motion changes may have potential to identify unsafe road users.