We present observations of XRF 050406, an X-ray flash with a relatively low fluence (∼ 10-7 erg cm-2 in the 15-350 keV band), a soft spectrum (photon index Γγ = 2.65), no significant flux above ∼ 50 keV and a peak energy Ep < 15 keV. XRF 050406 is the first burst detected by Swift clearly showing a flare in its X-ray light curve. The flare peaks 210 s after the BAT trigger, presents a flux variation δF/F ∼ 6 in a timescale δt/tpeak ≪ 1 and a measured fluence of 1-15% of the prompt one. We argue that the producing mechanism is late internal shocks, which implies that the central engine is still active at 210 s, though with a reduced power with respect to the prompt emission. The X-ray light curve flattens to a more shallow slope with a decay index of ∼ 0.5 after ∼ 4400 s, also supporting continued central engine activity.