The hybrid memory cube (HMC) is a 3-D-stacked DRAM architecture designed for substantially improved memory bandwidth. In particular, its I/O interface achieves up to 320 GB/s of external bandwidth through high-speed serial links. However, it comes at the cost of large static power of off-chip links, which dominates total power consumption of HMCs. In this paper, we propose an adaptive mechanism to partially disable off-chip links of HMCs to reduce the energy consumption of the off-chip links. In order to determine the number of the links to be disabled upon application loads, we develop a simple hardware module called link delay monitor to simulate all different link configurations at the same time and find the largest number of the links to be disabled while satisfying the given performance constraint. We also present two-level prefetching with in-HMC prefetch buffers to further improve the efficiency of our link power management scheme in the presence of prefetching. Evaluations show that our scheme reduces the energy consumption of HMCs by 52% on average with a negligible performance degradation.