We present near-infrared (IR) spectra of two planetary nebula (PN) candidates in close lines of sight toward the Galactic center (GC) using the Gemini Near-Infrared Spectrograph at Gemini North. High-resolution images from radio continuum and narrowband IR observations reveal ringlike or barrel-shaped morphologies of these objects, and their mid-IR spectra from the Spitzer Space Telescope exhibit rich emission lines from highly-excited species such as [S iv], [Ne iii], [Ne v], and [O iv]. We also derive elemental abundances using the Cloudy synthetic models, and find an excess amount of the s-process element krypton in both targets, which supports their nature as PNe. We estimate foreground extinction toward each object using near-IR hydrogen recombination lines, and find significant visual extinctions (A V > 20). The distances inferred from the size versus surface brightness relation of other PNe are 9.0 1.6 kpc and 7.6 1.6 kpc for SSTGC 580183 and SSTGC 588220, respectively. These observed properties along with the abundance patterns and close proximity to Sgr A∗ (projected distances ≲20 pc) make it highly probable that these objects are the first confirmed PN objects in the nuclear stellar disk. The apparent scarcity of such objects resembles the extremely low rate of PN formation in old stellar systems, but is in line with the current rate of sustained star formation activity in the Central Molecular Zone.