We present the results from a time domain study of absorption lines detected in quasar spectra with repeat observations from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7). Beginning with over 4,500 unique time separation baselines of various absorption line species identified in the SDSS DR7 quasar spectra, we create a catalogue of 2,522 quasar absorption line (QAL) systems with two to eight repeat observations, representing the largest, unbiased, and homogeneous collection of multi-epoch absorption systems ever published. To investigate these systems for time-variability of narrow absorption lines, we refine this sample based on the reliability of the system detection, the proximity of pixels with bright sky contamination to individual absorption lines, and the quality of the continuum fit. Variability measurements of this sub-sample based on the absorption line equivalent widths yield a total of 33 systems with indications of significantly variable absorption strengths on time-scales ranging from one day to several years in the rest frame of the absorption system. Of these, at least 10 are from a class known as intervening absorption systems caused by foreground galaxies along the line of sight to the background quasar. This is the first evidence of possible absorption line variability detected in intervening systems, and their short time-scale variations suggest that small-scale structures (~10-100AU) are likely to exist in their host foreground galaxies.