Aleksei Dudukalo misjudged his braking for Monza's first chicane and ploughed into the side of team-mate James Thompson after just two laps of Q1.
Thompson was able to rejoin and even set the ninth fastest time in Q2, giving him a front-row start for the second race.
Lada however has confirmed that the Briton will not take up that position as a result of the severity of damage done to his roll cage.
Team principal Viktor Shapovalov told AUTOSPORT that Dudukalo's car could be readied in time for the Monza races, but only at the cost of Thompson being ruled out of both Monza and potentially the next round in Marrakech.
Shapovalov said the team has therefore decided to withdraw both cars from the season's opening two races.
Dudukalo's participation in the Marrakech event is now uncertain.
"This is the first race for us so it's a big shame, but it is what it is," Shapovalov said.
"It's a blow but we will get over it. We could have had a strong second race but we don't have that chance.
"We know we are competitive. This is only one positive thing from this race. We will forget about it and concentrate on Marrakech."
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