Theoretical models predict that intermediate-mass black holes (IMBHs) exist in globular clusters (GCs), but observational evidence remains elusive. Millisecond pulsars (MSPs), which are abundant in GCs and have served as precise probes for gravitational waves, offer a unique opportunity to detect potential IMBH binaries in GCs. Here, we consider the possibility of using multiple MSPs in a GC to form a miniature pulsar timing array (PTA), so as to take advantage of their correlated timing residuals to search for potential IMBH binaries in the same cluster. Our semianalytical calculations reveal that nearby IMBH binaries around MSPs in GCs could induce microsecond-level timing residuals. In GCs like omega Centauri and M15, favorable configurations are found that could lead to the detection of binaries with mass ratios q >= 0.1 and orbital periods of a few days. We estimate that future higher-precision timing programs could achieve 100-ns sensitivity, substantially expanding the searchable parameter space and establishing mini-PTAs as powerful detectors of IMBHs.