It did not say how many votes were cast for each driver but noted "in the interests of fairness multiple votes identified as originating from the same source were not counted."
Formula One introduced the Driver of the Day award, the equivalent to football's 'Man of the Match', this year with the aim of increasing fan engagement in the sport.
Formula One media and other insiders had expressed fears that voting would reflect drivers' popularity on social media more than race-day performances.
Triple world champion Lewis Hamilton, who finished second behind team mate Nico Rosberg in a Mercedes one-two at Albert Park after starting on pole position, has over 3.2 million followers on Twitter.
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Grosjean has 549,000 while Manor's Indonesian rookie Rio Haryanto, the first Formula One driver from the nation of 250 million people, has acquired 423,000 in a matter of months. Haryanto failed to finish on Sunday.
"This is a win for us, this is a win," an emotional Grosjean had said on the team radio on Sunday after taking the chequered flag at the end of the team's debut race. "It feels like standing on the top step of the podium for us."
(Reporting by Alan Baldwin, editing by Ken Ferris)
