We report the measurement of spectral and spatial correlations in supercontinua generated by focusing microjoule pulses from a femtosecond ytterbium-doped fiber amplifier laser in bulk YAG. The measurement is full-bandwidth at a repetition rate of 1 MHz owing to the use of time-stretch dispersive Fourier transform technique. In contrast with fiber-based supercontinuum generation, our results show an excellent stability of the spectral and spatial properties of the output supercontinuum, with an essentially correlated behavior in the 1.4-1.7 μm wavelength range. These results provide strong ground for the development of supercontinuum-seeded ultrafast optical parametric amplifier systems in the mid-infrared using ytterbium lasers as pump sources.