Satellite synthetic aperture radar (SAR) images are recognized as one of the most efficient tools for day/night, all weather and large area monitoring of ships at sea. However, false alarms discrimination is still one key problem on SAR ship detection. While many discrimination techniques have been proposed for the treatment of false alarms, not enough emphasis has been targeted to explore how obtained false alarms are related to the changing ocean environmental conditions. To this end, we combined a large set of Sentinel-1 SAR images with ocean surface wind and wave data into one dataset. SAR images were separated into three distinct groups according to wave age (WA) conditions present during image acquisition: young wind sea, old wind sea, and swell. A constant false alarm rate (CFAR) ship detection algorithm was implemented based on the generalized gamma distribution (GΓD). Kolmogorov–Smirnov distance was used to analyze the distribution goodness-of-fit among distinct ocean environments. A backscattering analysis of different sizes of ship targets and sea clutter was further performed using the OpenSARShip and automatic identification system (AIS) datasets to assess its separability. We derived a discrimination threshold adjustment based on WA conditions and showed its efficacy to drastically reduce false alarms. To our present knowledge, the use of WA as part of the CFAR and for the adjustment of the threshold of detection is a novelty which could be tested and evaluated for different SAR sensors.