From what I've understood from reading different online sources including PSE*, measurements in quantum mechanics are generally argued to be irreversible (at least, when a macroscopic measuring device is used). This irreversibility is usually ascribed to an increase in total entropy (measured system $+$ measuring device) that occurs when the measurement is made. Quoting from the article "Irreversibility and Measurement in Quantum Mechanics" by Douglas M. Snyder:
Bohr (1935) maintained that quantum mechanical measurement also depended on the interaction between a macroscopic measuring instrument and the physical existent measured. He noted that when a macroscopical physical measuring apparatus is used, there is inevitably some loss of information concerning the measured system due to the resulting physical interaction. [...] For Bohr, once the information is lost in the measurement process, the measurement cannot be reversed.
However, this description only accounts for interaction-based measurements. What could we say about interaction-free measurements, then? (See the Wikipedia article for examples). If there is in those cases no physical interaction between the measuring instrument and the existent measured, by which mechanism could irreversibility be explained?