The inclusive $J/\psi$ production cross-section and fraction of $J/\psi$ mesons produced in B-hadron decays are measured in proton-proton collisions at $\sqrt{s} = 7$ TeV with the ATLAS detector at the LHC, as a function of the transverse momentum and rapidity of the J/psi, using 2.3$\textrm{pb}^{-1}$ of integrated luminosity. The cross section is measured from a minimum $p_T$ of 1 GeV to a maximum of 70 GeV and for rapidities within $|y| < 2.4$ giving the widest reach of any measurement of $J/\psi$ production to date.