  A $6.8 \ {\rm nb^{-1}}$ sample of $pp$ collision data collected under
low-luminosity conditions at $\sqrt{s} = 7$ TeV by the ATLAS detector at the
Large Hadron Collider is used to study diffractive dijet production. Events
containing at least two jets with $p_\mathrm{T} > 20$ GeV are selected and
analysed in terms of variables which discriminate between diffractive and
non-diffractive processes. Cross sections are measured differentially in
$\Delta\eta^F$, the size of the observable forward region of pseudorapidity
which is devoid of hadronic activity, and in an estimator, $\tilde{\xi}$, of
the fractional momentum loss of the proton assuming single diffractive
dissociation ($pp \rightarrow pX$). Model comparisons indicate a dominant
non-diffractive contribution up to moderately large $\Delta\eta^F$ and small
$\tilde{\xi}$, with a diffractive contribution which is significant at the
highest $\Delta\eta^F$ and the lowest $\tilde{\xi}$. The rapidity-gap survival
probability is estimated from comparisons of the data in this latter region
with predictions based on diffractive parton distribution functions.
