In the standard model of disk galaxy formation, a dark matter disk forms as massive satellites are preferentially dragged into the disk plane and dissolve. Here, we show the importance of the dark disk for direct dark matter detection. The low velocity of the dark disk with respect to the Earth enhances detection rates at low recoil energy. For weakly interacting massive particle (WIMP) masses M WIMP gsim 50 GeV/c 2, the detection rate increases by up to a factor of 3 in the 5-20 keV recoil energy range. Comparing this with rates at higher energy is sensitive to M WIMP, providing stronger mass constraints particularly for M WIMP gsim 100 GeV/c 2. The annual modulation signal is significantly boosted and the modulation phase is shifted by ~3 weeks relative to the dark halo. The variation of the observed phase with recoil energy determines M WIMP, once the dark disk properties are fixed by future astronomical surveys. The constraints on the WIMP interaction cross section from current experiments improve by factors of 1.4-3.5 when a typical contribution from the dark disk is included.