Given a set of existing points with their associated positive weights on the plane, the classical Fermat–Weber problem aims to find a new point that minimizes the overall weighted distances to the existing points. We investigate, in this paper, the Fermat–Weber problem with budgeted-uncertain interval point weights. The minmax regret criterion is applied to identify the meaningful solution. We first study some structural properties of the problem. Then, we develop an efficient algorithm to solve the corresponding problem, where the swarm-oriented algorithms are applied as subroutines. Computational results show the benchmarking results for these proposed methods. An examination is presented on identifying the minmax regret Fermat–Weber point concerning established a new airport in Vietnam, alongside its application in product transfer scenarios.