Fully enclosed noise barriers (FENBs) are increasingly being installed on high-speed railway bridges for noise pollution control. However, the aerodynamic effects of high-speed trains passing FENBs have an adverse impact on barrier durability and generate micro-pressure waves. In this paper, a numerical model of a train passing an FENB on a bridge is established. The aerodynamic pressure distribution along the FENB is analyzed for both a single train and two trains passing one another. The propagation characteristics and evolution mechanisms of pressure waves are then investigated. The results show that the pressure is lower at the ends of the FENB and higher in the middle along the direction of train travel. The peak positive and negative pressures at the mid-span are 1.95 and 4.47 times higher than those at the ends, respectively. This distribution is caused by the propagation, superposition, reflection, and attenuation of pressure waves. Compression waves account for 78.9% of the peak positive pressure. An amplification factor must be considered when estimating the impact of two trains passing one another. Analysis of five pressure-relief schemes shows that arranging a single pressure-relief hole at a high-pressure location effectively alleviates the over-pressure in the FENB. The overall pressure-relief effect is an exponential function of the single opening area. Considering a constant opening area, arranging several relief holes at equal spacing optimizes the adverse pressure distribution compared with the single-hole relief scheme. The equivalent forces of the multi-hole scheme are 3.35% and 7.58% lower than in the single-hole scheme.