The session was red-flagged to a halt after the four-time champion’s shunt, leaving runaway championship leader Lewis Hamilton in a perilous 15th place with just over two minutes remaining.
In a statement confirming the widely-expected move, Liberty Media said American Carey would take a position as the sport’s non-executive chairman.
Ferrari reverted back to an age-old burgundy livery for its 1,000th F1 race. But there was little to celebrate as Charles Leclerc finished eighth and Sebastian Vettel 10th.
Formula 1 2020: Lewis Hamilton grabs 95th career pole in Tuscan GP qualifying as Mercedes lock front row out
Bottas had been fastest in all three practice sessions, but he was unable to maintain his superiority over Hamilton in the decisive hour.
Formula 1 2020: Sebastian Vettel says he has 'no regrets' on Ferrari stint despite failing to win titles with team
Vettel made clear he felt revitalised by the prospect of joining Aston Martin next year— but looked back with pleasure on his years at Maranello.
After two disappointing races at Spa-Francorchamps and Monza, F1's first visit to the beautiful Ferrari-owned Mugello circuit in the rolling Tuscan hills marks Ferrari's achievement in being the first to enter 1,000 Grand Prix.
Formula 1 2020: Ferrari chief Mattia Binotto says team looking to put 'worst of days' behind at Mugello
Ferrari also finished outside the points in the previous race in Belgium and the second successive double flop dropped them to sixth in the constructors' championship.
Formula 1 2020: Pierre Gasly races to stunning victory at Italian GP as Lewis Hamilton handed penalty
Pierre Gasly finished 0.415 seconds ahead of McLaren driver Carlos Sainz and 3.358 ahead of Racing Point's Lance Stroll on a surreal-looking podium.
Racing Point said it had decided to accept the sanctions imposed and to move on, in the wider interests of the sport, following an agreement between all the teams on new rules to prevent any future 'reverse engineering' of other teams' cars.
Formula 1 2020: Lewis Hamilton aims to break records and Ferrari's heart at their home race in Monza
Lewis Hamilton will be favourite to claim his sixth victory in the old royal park, moving him one clear of the record five he now shares with Michael Schumacher – and leaving him on 90 wins overall ahead of the Tuscany Grand Prix a week later.
Formula 1 2020: Ferrari hurting after both drivers fail to qualify inside top 10 at Italian GP since 1984
After their pointless flop at the Belgian Grand Prix last Sunday, this was another embarrassment for the 'scarlet scuderia', but little surprise to their drivers.
Formula 1 2020: Lewis Hamilton claims pole position in Italian GP qualifying, Valtteri Bottas takes second
It was Hamilton’s record-increasing 94th career pole position, his sixth in seven races and his seventh in Italy.
Bottas was 0.229 seconds faster than Carlos Sainz and 0.323 quicker than Lando Norris after an impressive showing from the McLaren pair.
Formula 1 2020: Ferrari's Mattia Binotto admits he considered future with team after disappointing start to season
Mattia Binotto said he believed he retained the support of Ferrari's board and in particular chairman John Elkann and CEO Louis Camilleri.
Ex-Ferrari president Di Montezemolo said Vettel carried no blame for his and the team's struggles, adding that the team was not prepared for the sport's move to hybrid turbo engines in 2014.
Formula 1 2020: Mattia Binotto says Ferrari in the middle of a ‘storm’ ahead of home Italian GP, but denies ‘crisis’
Ferrari’s 2020 slump reached a new low on Saturday when after Vettel wound up last in third and final practice, the team faced the prospect of failing to progress from Q3 in qualifying.
Formula 1 2020: 'We have to stay calm' urges Sebastian Vettel after Ferrari's dismal performance at Belgian GP
Neither Vettel nor Leclerc was able to make any impression, as Ferrari struggled and finished pointless outside the top ten.
Formula 1 2020: Charles Leclerc warns Ferrari fans to not expect ‘any miracles’ at Belgian Grand Prix
Leclerc admitted he and the team had no explanation for the team's slump in form this season — ahead of the next two races which are scheduled to take place on homeground in Italy.
Formula 1 2020: Lewis Hamilton dedicates Belgian GP pole to late Black Panther star Chadwick Boseman
Meawnhile, things are going from terrible to abysmal for Ferrari, with Charles Leclerc in 13th and Sebastian Vettel 14th.
Verstappen clocked a best lap in one minute and 43.744 seconds to outpace the Australian by 0.048 seconds, leaving championship leader Lewis Hamilton down in third for Mercedes, 0.096 adrift of the pace-setter.