Diabetic neuropathy (DN) is a common complication of long-lasting type 1 and type 2 diabetes, with no curative treatment available. Here, we tested the effect of the incretin mimetic liraglutide in DN in mice with early-stage type 1 diabetes bred in a standard laboratory or enriched environment. With a single i.p. injection of streptozotocin 150 mg/kg, we induced murine diabetes. Liraglutide (0.4 mg/kg once daily, i.p. for ten days since the eighth post-streptozotocin day) failed to decrease the glycemia in the diabetic mice; however, it alleviated their antinociceptive behavior, as tested with formalin. The second phase of the formalin test had significantly lower results in liraglutide-treated mice reared in the enriched environment vs. liraglutide-treated mice under standard conditions [2.00 (0.00–11.00) vs. 29.00 (2.25–41.50) s, p = 0.016]. Liraglutide treatment, however, decreased the threshold of reactivity in the von Fray test. A significantly higher neopterin level was demonstrated in the diabetic control group compared to treatment-naïve controls and the liraglutide-treated diabetic mice (p < 0.001). The glutamine/glutamate ratio in both liraglutide-treated groups, either reared under standard conditions (p = 0.003) or an enriched environment (p = 0.002), was significantly higher than in the diabetic controls. This study demonstrates an early liraglutide effect on pain sensation in two streptozotocin-induced diabetes mouse models by reducing some inflammatory and oxidative stress parameters.