Use your scope probe to hold one end of a resistor in the 10K - 100K range. Probe the circuit with the open end of the resistor. It isolates your probe from the circuit. The amplitude will obviously be affected, but the frequency and wave shape will be unaffected.
Of course the wave shape will be affected, it's a low pass filter.
OP, you don't say what frequency you are talking about, or quantify "non-invasively", or say what you are trying to accomplish.
You can usually probe an AT crystal oscillator with a normal 10-15pF 10X scope probe.
If it's a tuning fork crystal, you need a 2-3pF active probe. With patience, you can find something like a Tek P6202 for a reasonable price. Or, build a simple JFET follower out of an MMBF4416.
If you designed the circuit yourself, add a buffer circuit to the board.