Tuesday's first-round match marks the start of Muguruza's campaign to become the sixth woman in the Open Era to win two back-to-back Wimbledon titles, reports Efe.
"I'm thinking to win, and to actually enjoy this time more," Muguruza said following the match, which lasted one hour and 28 minutes.
"I'm pretty happy with my serve, and controlling the emotions - to be back in a Grand Slam is always difficult, so I'm excited with the way I'm playing," Muguruza said after defeating Brody, world No. 138.
Muguruza is scheduled to square off against Alison Van Uytvanck of Belgium, world No. 47, who defeated Polona Hercog of Slovenia 6-2, 6-2.
Britain's Johanna Konta, world No. 24, and Slovakia's Dominika Cibulkova, world No. 33, both won their first-round matches, and are set to face off in the second round.
Konta eliminated world No.103 Natalia Vikhlyantseva of Russia 7-5, 7-6 (9-7) in one hour and 47 minutes, while Cibulkova needed one hour and 45 minutes to beat world No.44 Alize Cornet of France 7-6 (7-3), 6-1.
In other Wimbledon action, Spain's Lara Arruabarrena upset Ana Bogdan of Romania 6-1, 3-6, 8-6.
The world No.88 needed two hours and six minutes to defeat her world No.59 opponent, and heads the tournament's second round for the third time in her career.
Arruabarrena is set to take on world No.48 Su-Wei Hsieh of Taiwan, who earned an upset victory of her own on Tuesday after knocking out world No. 29 Anastasia Pavlyuchenkova of Russia 6-4, 4-6, 6-3.
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