Binge drinking of alcohol leads to worsened driving performance the following morning, even when the blood alcohol concentration (BAC) has returned to or is close to zero. The objective of this study was to investigate the effects of social drinking (BAC = 0.05%) on next-day driver fatigue and driving performance. A homogenous sample of 32 experienced male drivers drove for 35 min on rural and urban roads in a driving simulator, both the day after drinking alcohol and the day after a sober evening. The main effects on next-day performance were ambiguous, where self-assessments showed lower next-day performance and higher subjective sleepiness after drinking alcohol in the evening, whereas variability in lateral position, heart rate variability and attention showed worse next-day performance in the control condition. Overall, the effect sizes were small. The results indicate that a BAC level of 0.05% does not influence next-day performance after a full night’s sleep to any greater extent. Further studies including a placebo condition are needed to verify this result, also considering more BAC levels, long-term effects of habitual drinking, and longer driving times.