We use microlensing to probe the inner broad line region (BLR) of the lensed quasar SDSS J1004+4112, finding evidence of substructure. We study the recurrent microlensing events observed in the blue wing of the C IV emission line in image A of this lensed quasar from a series of 20 spectra taken over 15 yr. We obtain a microlensing light curve and confirm the presence of three high magnification events (∆m > ─0.7 mag). A caustic crossing is a natural explanation for each one of the events. The fast rising and fading of the events imply that the width of the region scanned by the caustic in each event, ≲0.1 μas (≲0.93 ± 0.36 light days), is much smaller than the BLR size. However, the large range of velocities involved implies significant overlapping with the inner BLR velocity field. An elongated thin substructure in the BLR fulfills both requirements at once. A sequence of caustics crossing a single elongated substructure may be a possible explanation of the observed recurrence. However, this hypothesis requires some ad hoc assumptions about the microlens population. Alternatively, a single caustic encountering several narrow-stripped or bow-shaped substructures in the approaching part of the BLR could explain the variability. We discuss the possible identification of these elongated substructures with ripples or spiral structure on the inner BLR. Simulations of caustic crossings of a rippled disk statistically support this interpretation. The study of the C IV emission-line variability in SDSS J1004+4112 illustrates the incomparable scanning power of microlensing in both velocity and space.