A method is proposed to generate low emittance electron bunches from two color laser pulses in a laser-plasma accelerator. A two-region gas structure is used, containing a short region of a high-Z gas (e.g., krypton) for ionization injection, followed by a longer region of a low-Z gas for post-acceleration. A long-laser-wavelength (e.g., 5 micron) pump pulse excites plasma wake without triggering the inner-shell electron ionization of the high-Z gas due to low electric fields. A short-laser-wavelength (e.g., 0.4 micron) injection pulse, located at a trapping phase of the wake, ionizes the inner-shell electrons of the high-Z gas, resulting in ionization-induced trapping. Compared with a single-pulse ionization injection, this scheme offers an order of magnitude smaller residual transverse momentum of the electron bunch, which is a result of the smaller vector potential amplitude of the injection pulse.