What should the voltage read when the pin it set to HIGH?
It could happen because the LED or any other components draw too much current than the MCU or the PSU can provide.
To my knowledge, ICs have a mechanism where their votlage drops when too much current is drawn from them.
I suggest that you first disconnect the LED from the GPIO pin and measure the voltage then.
If the voltage is still lower than how it should be, then there's probably something else thats overloading your system.