Mihajlovic, who as a player was regarded as one of the game's best-ever free kick specialists, had been in charge at the seven-times Italian champions for 18 months.
Torino, who have drawn 10 of their 19 league games this season, are 10th in Serie A.
Mazzarri's last job was at English Premier League club Watford in 2016-17 where they finished one place and six points above the relegation zone.
Before that, he had four seasons at Napoli, twice qualifying for the Champions League, and 18 months in charge of Inter Milan.
His first game as Torino coach will be at home to Bologna on Saturday.
Italian media said Mihajlovic, 48, had been told of the decision to sack him in the early hours of the morning and that a group of players had visited him to tell him that they stood by him.
"Torino announce the release of Sinisa Mihajlovic from his post of first-team coach," the club said in a brief statement.
"We thank Sinisa and his staff for the effort and passion he has shown in these 18 months."
There was no immediate comment from Mihajlovic himself.
Torino president Urbano Cairo said he was not happy with results this season and that the decision had nothing to do with Wednesday's game.
"We have strengthened the team but we have four points less than at the same point of last season," he told the Sportialia television channel. "We've been very inconsistent, among other things, and I didn't like the way things were going."
"It was a difficult decision - it's the first time in seven years we have fired a coach."
Torino was the sixth Serie A club of Mihajlovic's coaching career after Bologna, Catania, Fiorentina, Sampdoria and AC Milan, where he lasted less than one full season. He has also coached the Serbian national team.
Mihajlovic was sent off midway through the second half of Wednesday's game after protesting angrily at the referee's decision to award Juventus' second goal, a decision that the official stood by after studying the video replay system (VAR).
Torino claimed that midfielder Afriyie Acquah was fouled in the buildup to the goal.
Mihajlovic has mellowed in the last few years although still shows flashes of the fiery temper for which he used to be known.
Torino are the eighth Serie A club to switch coach this season after Cagliari, Benevento, Genoa, AC Milan, Sassuolo, Crotone and Udinese. Mihajlovic's predecessor Gian Piero Ventura was in charge from 2011 until 2016 when he left to coach Italy.
Ventura himself was sacked by Italy in November after they failed to qualify for the World Cup.
(Writing by Brian Homewood in Bern; Editing by Keith Weir/Jeremy Gaunt)
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