Nope, ringing is the effect of a high-pass (or band-pass) filter - it's the opposite of smoothing.
JPEG looses information by quantization, not low-passing. It is true that small high frequency coefficients will get rounded to 0 during quantization, and this does save quite a few bits. But the ringing is just from being imprecise about each DCT coefficient, coding a value that is either too large or too small.
Remember that a brickwall band pass filter (low, high, or anywhere else) is equivalent to convolution with this https://www.dsprelated.com/josimages_new/mdft/img1768.png in the spatial domain. Any time quantization is high enough for coefficients in a given band to become zero while the surrounding ones remain nonzero it will introduce at least some level of ringing.
wyager accurately described why in terms of the DCT though -- cosines naturally "ring" and the only way a non-sinusoid can be represented is through the combination of many other terms, so any time a coefficient contributing to this shape is eliminated, the structure "decays" so to speak and the underlying sinusoids become part of the reconstruction.
I don't think it makes sense to say that ringing is (necessarily) an effect of high-pass, low-pass, or band-pass filters. Any second-order system (that is undamped) could exhibit ringing. If I concatenate a low-pass filter with one of these ringing filters, I could get a ringing and low-pass filter
JPEG looses information by quantization, not low-passing. It is true that small high frequency coefficients will get rounded to 0 during quantization, and this does save quite a few bits. But the ringing is just from being imprecise about each DCT coefficient, coding a value that is either too large or too small.