The transverse polarization of Lambda and (Lambda) over bar hyperons produced in proton-proton collisions at a center-of-mass energy of 7 TeV is measured. The analysis uses 760 mu b(-1) of minimum bias data collected by the ATLAS detector at the LHC in the year 2010. The measured transverse polarization averaged over Feynman x(F) from 5 x 10(-5) to 0.01 and transverse momentum p(T) from 0.8 to 15 GeV is -0.010 +/- 0.005(stat) +/- 0.004(syst) for Lambda and 0.002 +/- 0.006(stat) +/- 0.004(syst) for (Lambda) over bar. It is also measured as a function of x(F) and p(T), but no significant dependence on these variables is observed. Prior to this measurement, the polarization was measured at fixed-target experiments with center-of-mass energies up to about 40 GeV. The ATLAS results are compatible with the extrapolation of a fit from previous measurements to the x(F) range covered by this measurement.