2D materials are considered for applications that require strong light-matter interaction because of the apparently giant oscillator strength of the exciton transitions in the absorbance spectrum. Nevertheless, the effective oscillator strengths of these transitions have been scarcely reported, nor is there a consistent interpretation of the obtained values. Here, we analyse the transition dipole moment and the ensuing oscillator strength of the exciton transition in 2D CdSe nanoplatelets by means of the optically induced Stark effect (OSE). Intriguingly, we find that the exciton absorption line reacts to a high intensity optical field as a transition with an oscillator strength F_Stark that is 50 times smaller than expected based on the linear absorption coefficient. We propose that the pronounced exciton absorption line should be seen as the sum of multiple, low oscillator strength transitions, rather than a single high oscillator strength one, a feat we assign to strong exciton center-of-mass localization. Within the quantum mechanical description of excitons, this 50-fold difference between both oscillator strengths corresponds to the ratio between the coherence area of the exciton’s center of mass and the total area, which yields a coherence area of a mere 6.1 nm². Since we find that the coherence area increases with reducing temperature, we conclude that thermal effects, related to lattice vibrations, contribute to exciton localization. In further support of this localization model, we show that F_Stark is independent of the nanoplatelet area, correctly predicts the radiative lifetime, and lines up for strongly confined quantum dot systems. [Figure not available: see fulltext.]