Nothing to worry about:
There is always stray capacitance around that will store electric charge and as your digital multimeter has a very high input impedance it will take a long time to discharge the charge.
The amplifier will certainly have some capacitors across the input lines which will store more charge, but the amplifier circuit will provide a discharge path in addition to the input resistance of the multimeter.
Put a 100K resistor or so across the input to the multimeter and measure again.
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PS: Some electronic products, especially hifi amplifiers, have massive capacitors across the supply lines and will continue to operate for a few seconds after the mains power has been switched off.