Background: The purpose of this research was to assess the growth, tolerance, and compliance outcomes associated with the consumption of a hydrolyzed rice infant formula (HRF) enriched with 2′-Fucosyllactose (2′-FL) a Human Milk Oligosaccharide (HMO), and nucleotides in an intended population of infants. Methods: This was a non-randomized single-group, multicenter study. The study formula was a hypoallergenic HRF with 2′-FL, Docosahexaenoic acid (DHA), Arachidonic acid (ARA), and nucleotides. Infants 0–90 days of age who were formula fed and experiencing persistent feeding intolerance symptoms, symptoms of suspected food protein (milk and/or soy) allergy, or other conditions where an extensively hydrolyzed infant formula was deemed an appropriate feeding option were recruited by pediatricians from their local populations. The primary outcome was maintenance of weight-for-age z-score. Weight, length, head circumference, formula intake, tolerance measures, clinical symptoms and questionnaires were collected. Thirty-three infants were enrolled, and 27 completed the study, on study product. Results: Weight-for-age z-scores of infants showed a statistically significant improvement from Visit 1 to Visit 4 (p = 0.0331). There was an adequate daily volume intake of 762 ± 28 mL/day, average daily number of stools of 2.1 ± 0.3, and mean rank stool consistency of 2.38 ± 0.18. After 28 days of switching to a HRF, 86.8 ± 5.9% of the symptoms resolved or got better by Visit 4 as reported by parents. Conclusions: HRF with 2′-FL HMO was safe, well tolerated, and supported weight gain in infants with suspected cow’s milk allergy or persistent feeding intolerance.