Objectives Prematurity, being small for gestational age and early neonatal ward admission are the major neonatal conditions that may interfere with breastfeeding supportive practices in infants born at gestational age ≥35+0 weeks. We aimed to investigate the associations between gestational age, small for gestational age, early neonatal ward admission and exclusive breastfeeding at one and four months. Methods A register-based cohort-study of all Danish singletons with gestational age ≥35+0 weeks born in 2014–2015. In Denmark, health visitors routinely conduct free home visits throughout infants’ first year and thereby report breastfeeding data to The Danish National Child Health Register. These data were linked with data from other national registers. Logistic regression models estimated the odds ratio for exclusive breastfeeding at one and four months, adjusted for confounding variables. Results The study population comprised 106,670 infants. Compared to gestational age 40 weeks, the adjusted odds ratio for exclusive breastfeeding at one month showed a decreasing tendency from gestational age ≥42 (n = 2,282) (1.07; 95% confidence interval (CI) 0.97–1.17) to 36 weeks (n = 2,062) (0.80; 95% CI 0.73–0.88). Small for gestational age (n = 2,342) was associated with decreased adjusted odds ratio for exclusive breastfeeding at one month (0.84; 95% CI 0.77–0.92). Neonatal ward admission was associated with increased adjusted odds ratio for exclusive breastfeeding at one month among late preterm infants (gestational age 35–36 weeks; n = 3,139) (1.31; 95% CI 1.12–1.54), as opposed to among early term (gestational age 37–38 weeks; n = 19,171) (0.84; 95% CI 0.77–0.92) and term infants (gestational age >38 weeks; n = 84,360) (0.89; 95% CI 0.83–0.94). The associations seemed to persist at four months. Conclusions Decreasing gestational age and small for gestational age were associated with decreased exclusive breastfeeding rates. Neonatal ward admission was associated with increased exclusive breastfeeding rates among late preterm infants, whereas the opposite was observed among early term and term infants.