Tubular fibers (raw and wax-free) from Ceiba pentandra (CP) were cross-linked with butane-1,2,3,4-tetracarboxylic acid (BTCA) at different concentrations to obtain a porous biodegradable medium for drug release applications. Chlorhexidine diacetate (CHX) was added to the cross-linked fibers for drug release studies. The Fourier transform infrared spectroscopy, thermogravimetric analysis, and scanning electron microscopy results indicated that the cross-linked fibers with a 5:1 fiber:BTCA ratio presented the higher cross-linking density. CHX was added at different concentrations (8% and 16% wt/wt); the elemental analysis indicated that CHX was loaded up to 7.99 wt%. In vitro studies showed a burst release of CHX within the first 3 h. CHX release kinetics was described using several models, with the Korsmeyer–Peppas equation, which adjusted better to the experimental data. The results indicated that the CP fibers are a feasible material for drug release applications.