Although several studies have aimed for accurate predictions of language recovery in post stroke aphasia, individual language outcomes remain hard to predict. Large-scale prediction models are built using data from patients mainly in the chronic phase after stroke, although it is clinically more relevant to consider data from the acute phase. Previous research has mainly focused on deficits, i.e., behavioral deficits or specific brain damage, rather than compensatory mechanisms, i.e., intact cognitive skills or undamaged brain regions. One such unexplored brain region that might support language (re)learning in aphasia is the hippocampus, a region that has commonly been associated with an individual’s learning potential, including statistical learning. This refers to a set of mechanisms upon which we rely heavily in daily life to learn a range of regularities across cognitive domains. Against this background, thirty-three patients with aphasia (22 males and 11 females, M = 69.76 years, SD = 10.57 years) were followed for 1 year in the acute (1–2 weeks), subacute (3–6 months) and chronic phase (9–12 months) post stroke. We evaluated the unique predictive value of early structural hippocampal measures for short-term and long-term language outcomes (measured by the ANELT). In addition, we investigated whether statistical learning abilities were intact in patients with aphasia using three different tasks: an auditory-linguistic and visual task based on the computation of transitional probabilities and a visuomotor serial reaction time task. Finally, we examined the association of individuals’ statistical learning potential with acute measures of hippocampal gray and white matter. Using Bayesian statistics, we found moderate evidence for the contribution of left hippocampal gray matter in the acute phase to the prediction of long-term language outcomes, over and above information on the lesion and the initial language deficit (measured by the ScreeLing). Non-linguistic statistical learning in patients with aphasia, measured in the subacute phase, was intact at the group level compared to 23 healthy older controls (8 males and 15 females, M = 74.09 years, SD = 6.76 years). Visuomotor statistical learning correlated with acute hippocampal gray and white matter. These findings reveal that particularly left hippocampal gray matter in the acute phase is a potential marker of language recovery after stroke, possibly through its statistical learning ability.