XRF 050416A was discovered by the Swift Burst Alert Telescope and re-pointed with the Swift narrow field instruments only 64.5 s after the burst onset. The 15 - 150 keV BAT average spectrum has a photon index of Γ ∼ 3.0 which classifies the bursts as an X-ray flash. The afterglow X-ray emission was monitored by the Swift X-Ray Telescope up to 74 days after the burst. The X-ray light curve shows a decay with three different phases: an initial steep decay with a decay slope of ∼ 2.4 (phase A), then, starting at ∼172 s from the burst onset, a second phase with a flat decay slope of ∼ 0.44 (phase B), and finally, after ∼1450 s from the burst onset, a third long-lasting phase with a decay slope of ∼ 0.88 (phase C). We find evidence of spectral evolution from a softer emission in the phase A of the afterglow decay, with Γ ∼ 3.0, to a harder emission with Γ ∼ 2.0 in the phases B and C. A redshift of 0.6535 was measured for the source. The spectra show intrinsic absorption in the host galaxy of ∼ 6.8 × 1021 cm-2. The consistency of the phase A photon index with the BAT photon index suggests that the initial fast decaying phase of the XRT afterglow might be the low energy tail of the prompt emission. The lack of jet break signatures in the X-ray afterglow light curve suggests very low collimation of the expanding fireball.