Massive multiple-input multiple-output (MIMO) systems have suffered from extremely high hardware complexity and cost because of the introduction of a tremendous number of antennas. Recently, one way to alleviate this is by considering the unequal uplink and downlink data transmission requirements and employing an asymmetrical transceiver. Such asymmetrical transceiver architecture, however, also brings out channel dimension inconsistency between the uplink and downlink. Thus, to well achieve the large array gain and fully exploit the potentials of asymmetrical transceiver-based massive MIMO systems, accurately recovering the full-dimensional downlink channel state information (CSI) based on the obtained small-dimensional uplink CSI is necessary. Nevertheless, the CSI at different antennas plays a different role in the CSI recovery due to the spatial correlation. Therefore, investigating appropriate antenna selection for asymmetrical transceiver-based massive MIMO systems is valuable and essential. To address this, we first formulate the antenna selection problem to minimize the mean-square recovery error of the full-dimensional downlink CSI in this paper. Then, two receive antenna selection algorithms are proposed by exploiting the low-rank property of the spatial correlation matrices under single-user scenarios. We also extend these algorithms to multi-user scenarios, and semi-closed-form optimal selection coefficients are derived. Numerical results demonstrate that, with the aid of the proposed antenna selection algorithms, the full-dimensional downlink CSI can be well recovered, which thus paves the way for asymmetrical transceiver-based massive MIMO systems to achieve their excellent downlink transmission performance with a much lower overall system hardware complexity and cost.