Hi CoolName,
First, are you hearing the spike? Or only questioning what's visible? You never mentioned if this was audible.
There are what could be a few causes, but let's consider 16khz, few people above the age of 35 yrs old can even hear. With that, you still want to kill any residual spike-like frequencies on your bass with a LPF (low pass filter). So a good cutoff frequency where you're still getting good punch, slap, harmonics etc. would be around 4k. That's being VERY considerate to just about any attainable sound from your bass. More like 2 kHz of LPF cuttoff would be more practical.
As to why that 16 kHertz spike is occuring could be a subtle transient, perhaps a leaky capacitor, maybe fretting buzz, or some issue with the coil winding. Maybe a non potted pickup, acting like a microphone and picking up some neighboring RF around your location (causing a spike). Maybe light fader which causes a buzz on that circuit in your house which is only a 60 cycle hum, but perhaps causing some spike. Poor shielding from the guitar, chord or connection might be a contributing culprit. Spikes are never a good thing, but that's why I ask if you can hear it?
While you're using filter cutoff, don't forget to set your HPF to around 60 to 80 hz as well.