Two X-ray sources were recently discovered by Irwin et al. that are compact companions to elliptical galaxies showing ultraluminous flares with fast rise (∼minute) and decay (∼hour), and with a peak luminosity ∼1040-41 erg s−1. Together with two other sources found earlier, they constitute a new type of fast transients that cannot be attributed to neutron stars, but might be due to intermediate-mass black holes (IMBHs; ). The flaring behavior is recurrent for at least two sources. If the flare represents a short period of accretion onto an IMBH during the periastron passage of a donor star on an eccentric (i.e., repeating) or parabolic (non-repeating) orbit, we argue that the flare's rise time corresponds to the duration during which the donor's tidally stripped mass joins a residual disk at the pericenter. This duration is in turn equal to three other timescales: the duration of stripping, the sound crossing time of the donor, and the circular orbit time at the pericenter radius. Only a white dwarf (WD) can have a sound crossing time as short as one minute. Therefore, the donor must be a WD and it was stripped of ∼10−10 M upon each passage at several to tens of Schwarzschild radii from the IMBH. The flux decay corresponds to the viscous drainage of the supplied mass toward the hole. Aided by long-term X-ray monitoring, this type of fast transient would be an ideal target for next-generation gravitational wave detectors.