A few handheld meters have a mV range with a very high impedance (e.g. > 1 GOhm) and in this case minute leakage and bias currents from the amplifier can charge up an open input. In this case it is absolutely normal than the voltage drifts and wanders if left open. No need for a repair.
One gets a similar effect with high end meters, where a high impedance input is standard.
If one want one could check the biasing current, by connecting something 10 M or 100 M to the input and than read the final voltage.
If not sensitive enough one could also use a low leakage capacitor (e.g. 10-100 nF PP) and use the speed at which the votage goes up to estimate the current.