This Letter presents a search for magnetic monopoles with the ATLAS detector at the CERN Large Hadron Collider using an integrated luminosity of $2.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of $pp$ collisions recorded at a center-of-mass energy of $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$. No event is found in the signal region, leading to an upper limit on the production cross section at 95% confidence level of $1.6/ϵ\text{ }\text{ }\mathrm{fb}$ for Dirac magnetic monopoles with the minimum unit magnetic charge and with mass between 200 GeV and 1500 GeV, where $ϵ$ is the monopole reconstruction efficiency. The efficiency $ϵ$ is high and uniform in the fiducial region given by pseudorapidity $|\ensuremath{\eta}|<1.37$ and transverse kinetic energy $600--700<{E}^{\mathrm{kin}}\mathrm{sin}\ensuremath{\theta}<1400\text{ }\text{ }\mathrm{GeV}$. The minimum value of 700 GeV is for monopoles of mass 200 GeV, whereas the minimum value of 600 GeV is applicable for higher mass monopoles. Therefore, the upper limit on the production cross section at 95% confidence level is 2 fb in this fiducial region. Assuming the kinematic distributions from Drell-Yan pair production of spin-$1/2$ Dirac magnetic monopoles, the efficiency is in the range 1%--10%, leading to an upper limit on the cross section at 95% confidence level that varies from 145 fb to 16 fb for monopoles with mass between 200 GeV and 1200 GeV. This limit is weaker than the fiducial limit because most of these monopoles lie outside the fiducial region.