The early-age hydration processes of concretes with mineral admixtures have been monitored and evaluated by a newly developed ultrasonic method based on embedded cement-based piezoelectric composite sensors. With the embedded ultrasonic (P-wave) measurement system, the waveform, wave velocity, attenuation coefficient index, and frequency-domain spectrum of detected ultrasonic waves during hydration can be recorded. The mineral admixtures examined include fly ash, slag, and silica fume, which replace part of the cement in concrete mixtures. It is found that the ultrasonic transmission parameters can be related to the microstructure changes of the concrete. Both the acceleration effects of silica fume and the retardation effects of fly ash and slag on the early hydration of concrete can be determined and explained through the analysis and comparison of the characteristics of the velocity curves. The attenuation coefficient index curve provides additional observation for the study of hydration kinetics. Moreover, the function of fresh concrete in filtering the high-frequency component of the wave varies with time, and concrete can be considered as low-pass frequency spectral filter. Frequency spectra analysis at different ages of fresh concrete provides useful information to reveal the early-age hydration process.