Kingsley Coman, Michael Olise and Thomas Mueller all netted twice, while Sacha Boey was also on target for the German champions in the game in Group C, which also features Boca Juniors and Benfica.
Harry Kane started but didn't find the target before being replaced just after the hour mark by Musiala, who netted his three goals in the space of 18 minutes towards the end.
It was a stroll in the park in the midday sun in Cincinnati for Vincent Kompany's side, with France winger Coman scoring twice in the opening 21 minutes either side of goals by compatriots Boey and Olise.
Coman's sixth-minute breakthrough goal was the first of the tournament following the 0-0 draw between Inter Miami and Al Ahly in Saturday's opening game.
Mueller got the fifth and Olise's second of the afternoon made it 6-0 in first-half stoppage time for the Bundesliga heavyweights.
Auckland City managed to stem the tide for much of the second half before Musiala came on and took centre stage, his three goals including one from the penalty spot.
Mueller made it 10-0 in the 89th minute for a Bayern side who won the Club World Cup twice in its former seven-team guise, in 2013 and 2020.
They have recorded bigger victories in the past in the German Cup, but the 10-goal winning margin equals their best ever win in the Bundesliga, when they beat Borussia Dortmund 11-1 in 1971.
Bayern, who gave new signing Jonathan Tah a debut in central defence following his recent arrival from Bayer Leverkusen, play Boca in their next match in Miami on Friday.
Auckland City take on Benfica earlier the same day in Orlando.
Match info and stats
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