Modern (sub-)millimeter interferometers enable the measurement of the cool gas and dust emission of high-redshift galaxies (z>5). However, at these redshifts the cosmic microwave background (CMB) temperature is higher, approaching, and even exceeding, the temperature of cold dust and molecular gas observed in the local Universe. In this paper, we discuss the impact of the warmer CMB on (sub-)millimeter observations of high-redshift galaxies. The CMB affects the observed (sub-)millimeter dust continuum and the line emission (e.g. carbon monoxide, CO) in two ways: (i) it provides an additional source of (both dust and gas) heating; and (ii) it is a non-negligible background against which the line and continuum emission are measured. We show that these two competing processes affect the way we interpret the dust and gas properties of high-redshift galaxies using spectral energy distribution models. We quantify these effects and provide correction factors to compute what fraction of the intrinsic dust (and line) emission can be detected against the CMB as a function of frequency, redshift and temperature. We discuss implications on the derived properties of high-redshift galaxies from (sub-)millimeter data. Specifically, the inferred dust and molecular gas masses can be severely underestimated for cold systems if the impact of the CMB is not properly taken into account. ; Comment: 13 pages, 11 figures. Accepted for publication in the Astrophysical Journal