Both drivers were also given a penalty point each after the two cars hit each other side on.
Stewards heard from both after the session, with the drivers agreeing what had happened was unnecessary and clumsy.
The stewards said in a statement they decided to escalate the penalty from the usual formal warning to a grid position drop because they had warned team managers earlier in the light of similar incidents this year between drivers in practice.
The pair — both contracted to Red Bull, which owns the two teams — went wheel to wheel 13 minutes into the session, with four-time world champion Verstappen diving down the inside of Lawson at Turn 12. The New Zealander held his ground through Turn 13 before they made contact.
The contact scattered debris across the track, with the session halted for it to be cleared.
Lawson and Verstappen were teammates at Red Bull this year while Isack Hadjar was injured and also briefly for two races at the start of last season.
"Maybe not very smart behaviour what he was trying to do there," Verstappen told reporters before seeing the stewards. "At the end of the day, it is not going to change my weekend, but if I were him, I would act a little smarter, and when you're fighting for your seat, it's not very smart behaviour.
"That's not very sensible behaviour from someone in his position, to pick a fight with me."
Lawson, who has yet to be confirmed by Racing Bulls for next season, said over the team radio, "He literally just drove into me."
Racing Bulls team boss Alan Permane was not impressed by either driver.
"One word — unnecessary. And I say that of both of them. I haven't heard what Max has said. I'm sure he's got his opinions and I'm sure Liam has his opinion. But mine is, it's just not needed and they can both do better," he told the BBC.
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