  We report on a thorough optical investigation of BaFe$_2$As$_2$ over a broad
spectral range and as a function of temperature, focusing our attention on its
spin-density-wave (SDW) phase transition at $T_{SDW}=135$ K. While
BaFe$_2$As$_2$ remains metallic at all temperatures, we observe a depletion in
the far infrared energy interval of the optical conductivity below $T_{SDW}$,
ascribed to the formation of a pseudogap-like feature in the excitation
spectrum. This is accompanied by the narrowing of the Drude term consistent
with the $dc$ transport results and suggestive of suppression of scattering
channels in the SDW state. About 20% of the spectral weight in the far infrared
energy interval is affected by the SDW phase transition.
