Adverse birth outcomes and infant undernutrition remain the leading causes of morbidity and mortality in sub-Saharan Africa (SSA). Impaired infant growth and development, which often begins during foetal development, may persist during the first 2 years of life and has been associated with higher risks of cardiometabolic diseases. This systematic review assessed the associations between maternal demographic characteristics and household socio-economic status (SES), and preterm birth (PTB), small for gestational age, low birth weight (LBW), stunting, wasting and underweight in children under 2 years of age in SSA countries. Following the Preferred Reporting Items for Systematic reviews and Meta-Analyses guidelines, we searched for publications in three electronic databases (PubMed, Scopus and ScienceDirect). Eleven studies on children under 2 years of age, in four SSA regions, published in English between 1990 and 2018, were included. All the studies were observational in design (cross-sectional or cohort studies). Maternal education was the most commonly explored exposure. Most studies (63.3%) focused on undernutrition during the first 2 years of life: LBW, PTB and stunting. Lower maternal education, maternal unemployment and lower household wealth index were the SES factors most commonly associated with adverse birth outcomes and infant undernutrition. Maternal marital status was not associated with any infant outcomes. The definitions of the SES varied, which may explain discrepancies between studies. Nutrition intervention programs in SSA need to promote education and poverty alleviation in women at reproductive age, starting from pre-pregnancy, to optimise infant growth and development and prevent the increase in the prevalence of cardiometabolic diseases.