Around half an hour into the session, the Italian had a high-speed spin at Turn 13 at the exit of Becketts, flat spotting his tyres and damaging his floor.
However, he was able to resume and returned to the pits under his own power, losing parts of the bodywork as he drove down the Hangar Straight towards Stowe.
That forced race control to red flag the session to allow marshals to clear the track before action was able to resume.
Giovinazzi was then reported under an FIA sporting regulation that states that "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".
After an investigation during the lunch break, he was given a warning under a new provision in the FIA's International Sporting Code.
A warning is a step above a reprimand and fine on the list of penalties. He is the first F1 driver to receive the sanction in 2020.
In their judgement, the stewards noted: "When the driver left the position where he had come to a stop at Turn 13 his car shed debris due to his damaged tyres.
"However, the Stewards felt that the driver acted in a manner that was potentially dangerous to other drivers when he continued at speed and without due caution to the pit lane, shedding debris along the way.
"That he did so also contributed to the extended twelve-minute suspension of the session.
"In deciding the penalty, the stewards have compared this incident to other practice incidents in the last few years and have elected to utilise the Warning that is newly available to them under the International Sporting Code."
Giovinazzi finished the session in 18th place, ahead of only Williams driver Nicholas Latifi and Ferrari's Sebastian Vettel, the latter having failed to set a time.