The invasion of aquifers into fractured gas reservoirs with edge water aquifers leads to rapid water production in gas wells, which reduces their gas production. Natural fractures accelerate this process. Traditional reservoir engineering methods cannot accurately describe the water influx, and it is difficult to quantitatively characterize the influence of aquifer energy and fracture development on production, which prevents aquifer intrusion from being effectively addressed. We divided the water influx of edge water aquifers in fractured gas reservoirs into three patterns: tongue-like intrusion in the matrix, tongue-like intrusion in fractures, and channel intrusion in fractures. Detailed numerical modeling of the water influx was performed using an embedded discrete fracture model (EDFM) to predict gas production. Because the strength of the aquifer and the conductivity of natural fractures have different effects on water influx, the effects of aquifers and natural fractures on the gas production of wells under the three water influx modes were studied. The results show that tongue-like intrusions lead to a stronger initial gas production of gas wells, which then become weaker after the wells are flooded, and the intrusions such as channeling in fractures cause the gas well to be flooded quickly. However, not all water influxes are unfavorable for gas production. Aquifers with water energy similar to gas formation and natural fractures with weak conductivity can improve the production of gas wells.