Background: Spinal cord injury (SCI) is a debilitating medical condition that can result in the irreversible loss of sensorimotor function. Current therapies fail to provide an effective recovery being crucial to develop more effective approaches. Mesenchymal stem cell (MSC) exosomes have been shown to be able to facilitate axonal growth and act as mediators to regulate neurogenesis and neuroprotection, holding great therapeutic potential in SCI conditions. This study aimed to assess the potential of human placental MSC (hpMSC)-derived exosomes on the functional recovery and reactivation of endogenous neurogenesis in an experimental animal model of SCI and to explore the possible mechanisms involved. Methods: The hpMSC-derived exosomes were extracted and transplanted in an experimental animal model of SCI with complete transection of the thoracic segment. Functional recovery, the expression of neural stem/progenitor cell markers and the occurrence of neurogenesis, was assessed 60 days after the treatment. In vitro, neural stem cells (NSCs) were incubated with the isolated exosomes for 24 h, and the phosphorylation levels of mitogen-activated protein kinase kinase (MEK), extracellular signal-regulated kinases (ERK), and cAMP response element binding (CREB) proteins were assessed by western blot. Results: Exosomes were successfully isolated and purified from hpMSCs. Intravenous injections of these purified exosomes significantly improved the locomotor activity and bladder dysfunction of SCI animals. Further study of the exosomes’ therapeutic action revealed that hpMSC-derived exosomes promoted the activation of proliferating endogenous neural stem/progenitor cells as denoted by the significant increase of spinal SOX2GFAP, PAX6Nestin, and SOX1KI67 cells. Moreover, animals treated with exosomes exhibited a significative higher neurogenesis, as indicated by the higher percentage of DCXMAP 2 neurons. In vitro, hpMSC-derived exosomes promoted the proliferation of NSCs and the increase of the phosphorylated levels of MEK, ERK, and CREB. Conclusions: This study provides evidence that the use of hpMSC-derived exosomes may constitute a promising therapeutic strategy for the treatment of SCI.