We present the results of a search for dark matter production in the monojet + missing transverse energy signature. We analyze a sample of Tevatron pp collisions at √(s) = 1.96 TeV, recorded by the CDF II detector, and corresponding to an integrated luminosity of 6.7fb-1. In events with significant missing transverse energy and one energetic jet, we find good agreement between the standard-model backgrounds and the observed data. We consider three modes of dark matter production: axial-vector mediated, vector mediated, and t-channel mediator exchange. In each mode, the mediator, M, couples to standard-model quarks and dark matter, where the dark matter (χ) is a Dirac fermion. We set 90% CL upper limits on 42 model points with varied values of mediator and dark matter mass between 0.96 and 42.8pb. The limits are translated into bounds on nucleon-dark matter scattering rates.