This study aimed to assess the impact of hypertensive disorders of pregnancy on infant neurodevelopment by comparing 6-month and 2-year psychomotor development outcomes of infants exposed to gestational hypertension (GH) or preeclampsia (PE) versus normotensive pregnancy (NTP). Participating infants were children of women enrolled in the Postpartum Physiology, Psychology and Paediatric (P4) cohort study who had NTPs, GH or PE. 6-month and 2-year Ages and Stages Questionnaires (ASQ-3) scores were categorised as passes or fails according to domain-specific values. For the 2-year Bayley Scales of Infant and Toddler Development (BSID-III) assessment, scores > 2 standard deviations below the mean in a domain were defined as developmental delay. Infants (n = 369, male = 190) exposed to PE (n = 75) versus GH (n = 20) and NTP (n = 274) were more likely to be born small for gestational age and premature. After adjustment, at 2 years, prematurity status was significantly associated with failing any domain of the ASQ-3 (p = 0.015), and maternal tertiary education with increased cognitive scores on the BSID-III (p = 0.013). However, PE and GH exposure were not associated with clinically significant risks of delayed infant neurodevelopment in this study. Larger, multicentre studies are required to further clarify early childhood neurodevelopmental outcomes following hypertensive pregnancies.