The GD-1 stellar stream exhibits spur and gap structures that may result from a close encounter with a dense substructure. When interpreted as a dark matter subhalo, the perturber is denser than predicted in the standard cold dark matter (CDM) model. In self-interacting dark matter (SIDM), however, a halo could evolve into a phase of gravothermal collapse, resulting in a higher central density than its CDM counterpart. We conduct high-resolution controlled N-body simulations to show that a collapsed SIDM halo could account for the GD-1 perturber's high density. We model a progenitor halo with a mass of 3 × 10⁸ M _⊙, motivated by a cosmological simulation of a Milky Way analog, and evolve it in the Milky Way's tidal field. For a cross section per mass of σ/m ≈ 30-100 cm² g^-1 at Vmax~10kms-1 , the enclosed mass of the SIDM halo within the inner 10 pc can be increased by more than 1 order of magnitude compared to its CDM counterpart, leading to a good agreement with the properties of the GD-1 perturber. Our findings indicate that stellar streams provide a novel probe into the self-interacting nature of dark matter.