(1) Background: Gentamicin is known to be nephrotoxic and ototoxic. Although gentamicin dosage guidelines have been established for preterm and term neonates, reports do show attainment of recommended peak concentrations but toxic gentamicin concentrations are common in this age group. (2) Methods: This was a prospective, observational study conducted in Namibia with 52 neonates. A dose of 5 mg/kg gentamicin was administered over 3–5 s every 24 h in combination with benzylpenicillin 100,000 IU/kg/12 h or ampicillin 50 mg/kg/8 h. Two blood samples were collected from each participant using a truncated pharmacokinetic sampling schedule. (3) Results: The one-compartment linear pharmacokinetic model best described the data. Birthweight, postnatal age, and white blood cell count were predictive of clearance (CL), while birthweight was predictive of volume (V). For the typical neonate (median weight 1.57 kg, median postnatal age 4 days (0.011 years), median log-transformed WBC of 2.39), predicted CL and V were 0.069 L/h and 0.417 L, respectively—similar to literature values. Simulated gentamicin concentrations varied with respect to postnatal age and bodyweight. (4) Conclusions: A 5 mg/kg/24 h dosage regimen yielded simulated gentamicin concentrations with respect to age and birthweight similar to those previously reported in the literature to be safe and efficacious, confirming its appropriateness.