The shocked 21-year-old rookie was unhurt in the incident between turns two and three but Williams said the chassis would have to be replaced, sidelining the Briton until Saturday's final session before qualifying.
Former world champions Williams are already facing plenty of problems with an uncompetitive car that is some way off their rivals' pace.
A loose drain cover halted first practice for the Azerbaijan Formula One Grand Prix on Friday after Williams driver George Russell ran over it at speed and destroyed the underside of his car.
The shocked 21-year-old rookie was unhurt in the incident between turns two and three but Williams said the chassis would have to be replaced, sidelining the Briton until Saturday's final session before qualifying.
"George's car will require a chassis change due to the damage caused by the loose drain cover," said a team spokeswoman.
"Therefore due to regulations he will not be able to run until practice three tomorrow."
Former world champions Williams are already facing plenty of problems with an uncompetitive car that is some way off their rivals' pace.
They are last in the standings and neither Russell nor Polish team mate Robert Kubica have scored a point in three races so far this year.
Russell won at the Baku street circuit last year on his way to the Formula Two title but Kubica has never raced there before and Williams need all the track time they can get.
"I just hit it, the biggest shock went through my body. The whole engine just turned off, it's ruined the floor," said Russell.
"It was just on the normal racing line and has ruined my session."
The session was red flagged and then abandoned just 12 minutes into the scheduled 90 as organisers and track officials worked to check more than 300 manhole covers and carry out repairs.
"They're going to fix it (the track) now but of course it shouldn't have happened," said Red Bull's Max Verstappen. "Running over a cover like that at 300 kph is not nice."
In more farcical scenes, the mobile crane truck carrying Russell's stricken Williams back to the pits then hit the underside of a sponsor hoarding spanning the track, leaking fluid onto the car.
Ferrari's two drivers were the only ones to set a time, with Charles Leclerc ahead of Sebastian Vettel. Replays showed the Monegasque running over the cover, potentially dislodging it, just before Russell.
Five-times world champion and overall leader Lewis Hamilton, winner in Baku last year for Mercedes, did not seem to mind the lack of action, however.
"How could they have not checked and sealed the drains?" the Briton asked on his Instagram feed.
"Oh well, (it) just gives me extra time to catch up on Game of Thrones," added the 34-year-old, who has been binge-watching the popular fantasy series.
The second practice session was scheduled to get underway at 1700 local time (1300 GMT).
