Inducing a magnetic gap at the Dirac point of the topological surface state (TSS) in a three-dimensional (3D) topological insulator (TI) is a route to dissipationless charge and spin currents. Ideally, magnetic order is present only at the surface, as through proximity of a ferromagnetic (FM) layer. However, experimental evidence of such a proximity-induced Dirac mass gap is missing, likely due to an insufficient overlap of TSS and the FM subsystem. Here, we take a different approach, namely ferromagnetic extension (FME), using a thin film of the 3D TI Bi2Te3, interfaced with a monolayer of the lattice-matched van der Waals ferromagnet MnBi2Te4. Robust 2D ferromagnetism with out-of-plane anisotropy and a critical temperature of Tc≈15 K is demonstrated by x-ray magnetic dichroism and electrical transport measurements. Using angle-resolved photoelectron spectroscopy, we observe the opening of a sizable magnetic gap in the 2D FM phase, while the surface remains gapless in the paramagnetic phase above Tc. Ferromagnetic extension paves the way to explore the interplay of strictly 2D magnetism and topological surface states, providing perspectives for realizing robust quantum anomalous Hall and chiral Majorana states.