You can measure the internal resistance of a multimeter using megger tester.
As you can see in this video, $5 DMM is not accurate and lower internal resistance(1MΩ). So, it will more influence on the measured circuit.
Another method is using series resistor.
This resistor in combination with the internal resistance will form a voltage divider.
If you apply 5V over a 1M series resistor, and the DMM shows it as 2.5V, then the internal resistance is 1MΩ