Direct measurement of the modulation transfer function (MTF) of focal plane arrays (FPAs) using random laser speckle approaches for the visible/near-infrared wavelength band has been well documented over the last 20 years. These methods have not transitioned to the midwave infrared (MWIR) primarily because other techniques have been sufficient and MWIR laser sources with sufficient output power have been unavailable. However, as the detector pitch decreases, MTF measurements become more difficult due to diffraction, while potential MTF degradation due to lateral carrier diffusion crosstalk makes accurate MTF characterization critical for sensor system design. Here, a random laser speckle FPA MTF measurement approach is adapted for use in the MWIR that utilizes a quantum cascade laser coupled with an integrating sphere to generate the appropriate in-band random speckle. Specific challenges associated with the technique are addressed including the validity of the Fresnel diffraction assumptions describing the propagation of the random speckle field from the integrating sphere to the FPA. Improved methods for estimating the power spectral density (PSD) of the measured speckle that reduce data requirements are presented. The statistics and uniformity of the laser speckle are presented along with PSD measurements and estimated MTFs of a MWIR FPA.