a resistor based voltage divider requires some current to flow, it doesn't have to flow to ground, and you can adjust what the resistances are to change how much total current is drawn, but for what your describing, it would likely end up to ground
also add to this that your arduino's ADC generally cannot handle large value resistances before its readings start to skew you need to generally approach it with an Op Amp
Ok so lets use an op amp, I do not know how high a voltage you need to divide, but lets say its something reasonable e.g. 10V, in this case, if you can power the op amp from a voltage higher than this signal, you can use it to buffer it, it has 10V on its + input, and it outputs a fixed 10V on its output, while only drawing a tiny current e.g. 1nA, you can then use a normal low value resistor divider inside your device,
simulate this circuit – Schematic created using CircuitLab
If the external voltage is much higher, you can still use this to make a divider with larger resistors and a lower current drawn from your signal, e.g. lets say you wanted to measure 50V, with that op amp, you could divide that down 10:1 with large resistors around say 1 million ohms for the input and 110,000 ohms for the lower leg of the divider, the op amp then buffers this to your arduino drawing only a small amount of current from the signal, in this case about 40uA
simulate this circuit
And as a work around to the other answer, while more difficult, you can use an op amp as a differential amplifier, so instead of connecting the arduinos ground to the outside world, you end up with 2 inputs, where your measuring the difference between them,