Massive multiple-input multiple-output (MIMO) systems, which utilize a large number of antennas at the base station, are expected to enhance network throughput by enabling improved multiuser MIMO techniques. To deploy many antennas in reasonable form factors, base stations are expected to employ antenna arrays in both horizontal and vertical dimensions, which is known as full-dimensional (FD) MIMO. The most popular two-dimensional array is the uniform planar array (UPA), where antennas are placed in a grid pattern. To exploit the full benefit of massive MIMO in frequency division duplexing, the downlink channel state information (CSI) should be estimated, quantized, and fed hack from the receiver to the transmitter. However, it is difficult to accurately quantize the channel in a computationally efficient manner due to the high dimensionality of the massive MIMO channel. In this paper, we develop both narrow-hand and wideband CSI quantizers for FD-MIMO taking the properties of realistic channels and the UPA into consideration. To improve quantization quality, we focus on not only quantizing dominant radio paths in the channel, but also combining the quantized beams. We also develop a hierarchical beam search approach, which scans both vertical and horizontal domains jointly with moderate computational complexity. Numerical simulations verify that the performance of the proposed quantizers is better than that of previous CSI quantization techniques.