A solid base catalyst comprising pyridine-palladium polyorganosiloxane framework was synthesized via a grafting method. The resulting organic–inorganic hybrid palladium nanomaterial was characterized by 13C CP-MAS NMR, 29Si CP-MAS NMR, XRD, EDX, TEM, TGA, and the BET measurements. The hybrid palladium nanomaterial exhibited high catalytic activity for the Suzuki–Miyaura cross-coupling reaction between aryl chlorides and phenylboronic acid under base-free and aerobic conditions. A maximum turnover number (TON) of 3150, with a 0.2 mol% Pd loading and a reaction temperature of 80 °C in aqueous solution. The catalyst demonstrated remarkable stability, maintaining its activity even after six cycles of reuse without significant loss of activity. TEM images showed that the catalyst retained its structure and high-order mesostructure after several uses. ICP-AES also confirmed the absence of palladium contamination in the final products. Leaching test studies further confirmed the true heterogeneous nature of the developed catalytic system.