A muffling apparatus capable of attaining the prevention of the occurrence of a noise reliably while making concrete the reduction of the manufacturing cost and the easiness of the assembling of the same apparatus, and a feed water apparatus having such a muffling effect are provided. The muffling apparatus 2 is an apparatus connected to a jet pipe 1 adapted to send out the water, which flows in a feed water passage 1a in the interior thereof, into storage water W. The apparatus has a tubular portion 4 connected to an upstream side portion of the jet pipe 1 so that the tubular portion 4 extend downward, and having therein a water supply passage 4a communicating with the feed water passage 1a, and a housing 3 connected water-tightly to an upstream side portion of the jet pipe 1 and an upper section of the tubular portion 4, enclosing a lower section of the tubular portion 4, connected water-tightly to a downstream side portion of the jet pipe 1, and capable of storing the air, which is in the interior of the jet pipe 1, in the portion of the interior of the housing 3 which is outside the tubular portion 4. The tubular portion 4 is provided at an upper section thereof with an air hole 4b made through a wall thereof so as to communicate the water supply passage 4a with the interior of the housing 3.