Whisk together first 5 ingredients in a large bowl; slowly pour in oil, whisking constantly.
Rinse fennel. Trim stalks to within 1" of end. Discard hard outside stalks. Remove tough core from bottom of bulb. Starting at 1 side, cut bulb vertically into thin shreds.
Add fennel, apple, and celery to dressing, tossing to combine. Cover and chill up to 4 hours. Toss well just before serving.