The cross section for dijet production in proton-proton collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ is presented as a function of $\stackrel{\texttildelow{}}{\ensuremath{\xi}}$, a variable that approximates the fractional momentum loss of the scattered proton in single-diffractive events. The analysis is based on an integrated luminosity of $2.7\text{ }\text{ }{\mathrm{nb}}^{\ensuremath{-}1}$ collected with the CMS detector at the LHC at low instantaneous luminosities, and uses events with jet transverse momentum of at least 20 GeV. The dijet cross section results are compared to the predictions of diffractive and nondiffractive models. The low-$\stackrel{\texttildelow{}}{\ensuremath{\xi}}$ data show a significant contribution from diffractive dijet production, observed for the first time at the LHC. The associated rapidity gap survival probability is estimated.