Radar micro-Doppler (m-D) signature, which reflects the micromotion dynamic and structural characteristics of radar target with micromotion, has received increasing attention. Most of the existing m-D signature-extraction methods operate in the time domain or the time-frequency domain. Different from these methods, in this paper, an m-D period estimation approach that operates in the ambiguity domain is proposed. Although the ambiguity function (AF) has been widely used in the field of radar signal processing, its application for m-D signal is introduced for the first time. It is proved that the AF of m-D signal exhibits periodicity along the lag axis and has the best concentration when the lag equals to multiples of the m-D period. Based on this, three AF concentration statistics are employed to capture the periodicity and to provide the m-D estimate. The most important property of the AF concentration statistics is that they are (or approximately) invariant to polynomial translations with terms not larger than second order even if the signal is Doppler ambiguous. Numeric simulation and real radar experiments are used to validate the effectiveness of the proposed technique.