A search has been made for events containing an energetic jet and an imbalance in transverse momentum using a data sample of pp collisions at a center-of-mass energy of 7 TeV. This signature is common to both dark matter and extra dimensions models. The data were collected by the CMS detector at the LHC and correspond to an integrated luminosity of 5.0 fb(-1). The number of observed events is consistent with the standard model expectation. Constraints on the dark matter-nucleon scattering cross sections are determined for both spin-independent and spin-dependent interaction models. For the spin-independent model, these are the most constraining limits for a dark matter particle with mass below 3.5 GeV/c(2), a region unexplored by direct detection experiments. For the spin-dependent model, these are the most stringent constraints over the 0.1-200 GeV/c(2) mass range. The constraints on the Arkani-Hamed, Dimopoulos, and Dvali model parameter M D determined as a function of the number of extra dimensions are also an improvement over the previous results.