This study assessed the magnitude of hidden hunger (micronutrient deficiencies) and cognitive deficits of 130 school-aged children (6–13 years old) living in three selected orphanages in Kumasi, Ghana. Sociodemographic data assessment, anthropometric assessment (BMI for age and height for age), dietary assessment (3-day repeated 24-hour dietary recall), urinary iodine level assessment, and cognitive performance assessment (Raven’s Coloured Progressive Matrices) were performed. Boys formed 50.8% of the study population, while girls formed 49.2%. The median age of participants was 10.50 years. About 12.3%, 7%, and 10.0% of participants were stunted, thin, and overweight/obese, respectively. The prevalence of mild iodine deficiency (i.e., 50–99 μg/L) was 16.2%. Iodine deficiency was significantly higher (23.6%) in participants who had lived for at least 7 years in the orphanage compared to those who had lived less than 7 years (10.7%) (
p
=
0.047
). About 17% of the participants performed poorly (<50%) on the cognition test. Mean cognition test scores were significantly different among the orphanages (
p
=
0.027
). The majority of participants, 89.2%, 54.6%, 76.9%, and 77.7%, had adequate intake of iron, zinc, vitamin C, and folate, respectively, whereas intake of vitamins A and B12 was inadequate for the majority of participants (90.8% and 50.8%, respectively). There was no significant correlation between micronutrient intake and cognitive performance. However, mean cognition test scores were significantly different between participants with adequate and inadequate iron and vitamin A intake (
p
=
0.007
and
p
<
0.001
, respectively). The findings of this study warrant a closer look at nutritional intakes in orphanages to improve hidden hunger and cognitive performance.