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We consider the dephasing rate of an electron level in a quantum dot placed next to a fluctuating edge current in the fractional quantum Hall effect. Using perturbation theory, we show that this rate has an anomalous dependence on the bias voltage applied to the neighboring quantum point contact, which originates from the Luttinger liquid physics which describes the Hall fluid. General expressions are obtained using a screened Coulomb interaction. The dephasing rate is strictly proportional to the zero-frequency backscattering current noise, which allows us to describe exactly the weak to strong backscattering crossover using the Bethe-ansatz solution.

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