Pioneer 10 and 11 were the first probes sent to study the outer planets of the Solar System, and Pioneer 10 was the first spacecraft to leave the Solar System. Besides their already epic journeys, Pioneer 10 and 11 spacecraft were subjected to an unaccounted effect interpreted as a constant acceleration towards the Sun, the so-called Pioneer anomaly. One of the possibilities put forward for explaining the Pioneer anomaly is the gravitational acceleration of the Kuiper Belt. In this work we examine this hypothesis for various models for the Kuiper Belt mass distribution. We find that the gravitational effect due to the Kuiper Belt cannot account for the Pioneer anomaly. Furthermore, we have also studied the hypothesis that drag forces can explain the Pioneer anomaly; however, we conclude that the density required for producing the Pioneer anomaly is many orders of magnitude greater than those of interplanetary and interstellar dust. Our conclusions suggest that only through a mission can the Pioneer anomaly be confirmed and further investigated. If a mission with these aims is ever sent to space, it turns out, on account of our results, that it will also be a quite interesting probe to study the mass distribution of the Kuiper Belt.