Ambient backscatter devices (tags and readers) use existing radio frequency (RF) signals to transmit data. Most prior works consider single-antenna tags, but this paper investigates the case of multiple-antenna tags, which are capable of simultaneous energy harvesting and data transmission. However, the multi-antenna channel between the tag and the reader, and the unpredictable nature of RF signals due to uncontrollable RF sources (e.g., location and transmit power), make signal detection highly challenging. Thus, the detection process becomes a hypothesis testing problem with unknown parameters. Consequently, we design a blind detector based on the generalized likelihood ratio test (GLRT) without using channel state information (CSI), signal power and noise variance. The decision threshold and detection probability of it are also analyzed in detail. Furthermore, to maximize its detection performance, we develop the optimal backscatter antenna selection scheme. Interestingly, we show that the detector performs best when only two backscatter antennas are selected. Finally, extensive simulation results validate the analysis and illustrate the effectiveness of the proposed detector.