The Sauber driver turned in on Piastri during the opening segment of Sprint Qualifying on Friday afternoon (local time) in Miami.
Bottas was on a slow lap while the McLaren behind him was starting a flying lap.
Piastri quickly closed on the Finn, moving to the inside to take the apex only for the Sauber to turn into the right-hander.
The pair came close but avoided contact.
Stewards investigated the near miss following the session and found Bottas to have breached Article 33.4 of the Sporting Regulations.
Article 33.4, FIA Formula 1 Sporting Regulations
At no time may a car be driven unnecessarily slowly, erratically or in a manner which could be deemed potentially dangerous to other drivers or any other person.
“On the straight before Turn 1, Car 77 was being driven slowly on the racing line after finishing a fast lap, while Car 81 was approaching on a fast lap. Car 81 and Car 77 needed to take evasive action to avoid a collision,” the infringement notice explained.
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“The primary responsibility rests with the driver to ensure that he does not place himself in a position whereby he unnecessarily impedes another driver.
“Here Car 77 was driving slowly on the racing line and caused to the situation that ensued.
“However, during the hearing both team and driver of Car 77 admitted that the team had not warned the driver of Car 77 that Car 81 was approaching on a fast lap.
“That was obviously an error on the team’s part and contributed significantly to the incident.
“In light of the above, we impose a penalty of a drop of 3 grid positions at the race.”
Bottas, who has a new race engineer this weekend, falls from 18th on the Sprint starting grid to last as a result of the penalty.
The Miami Sprint begins at noon local time on Saturday (Sunday 02:00 AEST).
Elsewhere, Mercedes escaped penalty following an investigation into a pit lane infringement.
Mechanics for Lewis Hamilton were in the pit lane without their complete safety attire.
While noting the team was in breach of the regulations, it was let off without any further action as officials noted it was not alone in its practices.
“As we were examining the conduct of the team in relation to this infringement (which was reported to us by Race Control), it came to our attention that a number of other teams had engaged in similar work without helmets and/or without eye protection during the session either within the pit stop position or in close proximity to it,” stewards noted.
“Certainly, those that were working on the car within the pit stop positions would also have been in breach of Article 34.13 (for example by touching the car or jacking up the car).
“Indeed, those slightly outside of their pit stop position may not been in breach of the above article but the distinction, from a safety perspective (which is the likely purpose for this rule), was not obvious to us.
“Furthermore, it appears to be the established practice to jack the car up, while blowers are used to cool the brakes, within the pit stop position to bring the car back into the garage.
“That too, read strictly, could be in breach of the above regulations.
“So, in these circumstances, penalising one team, where all or nearly all the teams may potentially have been in breach of this article in some form or the other would not The Stewards serve a useful purpose.
“We accordingly took no further action. However, we request the FIA to consider whether changes need to be made to either the current practices during Qualifying/Sprint Qualifying or the regulations themselves.”
It is not the first time such a transgression has occurred.
Teams were warned following last year’s Abu Dhabi Grand Prix when mechanics from several teams did not wear eye protection during pit stops.
In that instance, Mercedes was one of three teams referred to the stewards.
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