Just like high-bandwidth scopes, spectrum analyzers are usually low impedance. It gets increasingly hard to develop high-impedance inputs at higher frequencies. At 1 GHz, even 1 pF of shunt capacitance will result in an impedance of about 160 ohm. Not much point putting a 1 Mohm resistor in parallel with this, is there? High-impedance probes also get difficult since impedance and reflections get hard to control without using transmission lines. Try to calculate what a 1 Mohm transmission line would look like on a common FR-4 layer stack-up or as coax with common dielectrics. Few if any probes driving high-impedance inputs go beyond 500 MHz, most spectrum analyzers go much higher. Even those expensive 500 MHz passive hi-Z probes don't work terribly well, loading at 500 MHz is much higher than passive Z0 (50 ohm) probes, and similar to a plain 50 ohm input.
If you need less DC loading, use a $$$ active probe. If you just need less high-frequency loading, a Z0 probe like Janne suggests should be able to get quite close in performance. In many cases, you may not need a probe at all. If all you need are relative measurements or you can deal with calibration yourself, just using a piece of coax with some of the shielding removed should make an acceptable antenna. I wouldn't expect excellent flatness across the bandwith of the specan with it, but it is very unlikely to destroy the front-end this way.