We present the results of proper-motion measurements of the dust shell structure in the Egg Nebula (AFGL 2688, CRL 2688, V1610 Cyg), based on the archived two-epoch data at 2 μm taken with the Hubble Space Telescope. We measured the amount of motion of local structures in the nebula by determining their relative shifts over an interval of 5.5 yr. The dynamical age of the nebula is found to be roughly 350 yr based on the overall Hubble-law-esque motion of the nebula. By adopting the deprojected velocity of 45 km s^-1 at the tips of the bipolar lobes, our proper-motion measurements indicate that the distance to the Egg Nebula is about 420 pc and that the lobes are inclined at 77 with respect to the plane of the sky. The refined distance estimate yields a luminosity of the central star of 3.3 × 10³ L, a total shell mass of 1.2 M, and a mass-loss rate (the upper limit) of 3.6 × 10^-3 M yr^-1. Assuming a 0.6 M central post-AGB stellar mass, the initial mass of the Egg is 1.8 M. Upon analysis, we also discovered that (1) the central star of the Egg Nebula has a proper motion of its own at a rate of 17 mas yr^-1, (2) the tips of the lobes increased their velocity due to shock acceleration, and (3) the apparent bipolar lobes consist of multiple outflows at distinct inclination angles projected onto each other.