Russell sped through the final two corners seconds after Verstappen went spinning off the track toward the barrier, causing a yellow flag which means drivers must slow down.
Russell was warned of the yellow flag ahead of time by Mercedes over the radio and argued that he lifted off the accelerator earlier than usual for the corner and that the rest of his lap was still enough for first place.
The stewards agreed and deemed the incident needed "no further investigation". It wasn't immediately clear if other teams planned to protest.
"I saw the yellow, I had a big lift into the corner... it was a single yellow and should be okay," said Russell, who continued Mercedes's streak of securing pole position for the eighth race in a row.
Verstappen's earlier time was still good enough for fifth ahead of the McLarens of Lando Norris and Piastri, who admitted he had "been pushing hard in qualifying".
Until Russell's run, Ferrari's Charles Leclerc and Lewis Hamilton were set to end Mercedes' run of pole position in each grand prix this season.
They both bested Formula One standings leader Kimi Antonelli's time by less than a tenth of a second shortly before Verstappen went off.
Verstappen had also looked like a contender for pole with his upgraded Red Bull car and was set to improve on his previous time.
Leclerc is set to start Sunday's race second, and Hamilton third after his win for Ferrari last time out. Antonelli was fourth in his lowest qualifying result of the season.
Russell has not won a grand prix proper since the season-opener in Australia. The next five races were won by Antonelli before the Italian teenager failed to finish two weeks ago in Barcelona where Hamilton triumphed.
Antonelli tops the championship 41 points ahead of Hamilton and 50 ahead of Russell.
Mercedes team principal Toto Wolff told Sky Sport Germany it was "a matter of experience" that Antonelli seemed to abandon his lap after Verstappen's crash while Russell was "super clever" in lifting off just enough to keep his lap competitive.
