Like Greg said, a note played can make an open string ring sympathetically. It’s not a bad thing to have a violin ring nicely when played, although there might be something off kilter if you’re only getting good response from that one note.
Make sure you’re not accidentally hitting the D string with your bow while playing on the A. If you find that you can’t play on only one string, the bridge is probably too flat.
When you play a really powerful violin, the vibrations can be significant enough that you’ll feel them through your jawbone.
That said, if it's just that note, could be annoying or problematic. Esp, to play in other keys, generally want instrument to have a more even sound.
Violins can have resonant hot spots, or wolf tones... independent of sympathetic string vibration... resonance of the body, wood, cavity and the set up (bridge tuning, soundpost, perhaps strings?). Often seems the cavity (hum test) is more around C#.
Can be tough to tame those hot notes; not sure of any easy fix, and might want to have a luthier check it over to see if can make adjustments. A soundpost adjustment, and bridge fine tuning trim (took a few attempts)... helped one of my fiddles.