The design of hydrogels for the controlled release of active species is an attractive challenge. In this work, we prepared hybrid hydrogels composed of halloysite nanotubes as the inorganic component, and alginate as the organic counterpart. The reported procedure allowed us to provide the resulting materials with a peculiar wire-like shape. Both optical and scanning electron microscopy were used to characterize the morphological properties of the hydrogel wires, whose diameters were ca. 0.19 and 0.47 mm, respectively. The possibility to be exploited as drug delivery systems was carried out by loading the nanoclay with salicylic acid and by studying the release profiles. Thermogravimetric experiments showed that the amount of encapsulated drug was 4.35 wt%, and the salicylic acid was thermally stabilized after the loading into the nanotubes, as observed by the shift of the degradation peak in the differential thermograms from 193 to 267 °C. The kinetics investigation was conducted using UV–Vis spectrophotometry, and it exhibited the profound effects of both the morphology and dimensions on the release of the drugs. In particular, the release of 50% of the payload occurred in 6 and 10 h for the filiform hydrogels, and it was slower compared to the bare drug-loaded halloysite, which occurred in 2 h. Finally, an induction period of 2 h was observed in the release profile from the thicker sample.