The 24-year-old winger netted in the Reds' opening day draw at Watford and in wins over Crystal Palace and Arsenal to help Jürgen Klopp's charges record a strong start to the new campaign.
Although irrelevant to his domestic award, Mané also helped steer Liverpool into the Champions League group stages as they overcame German side Hoffenheim 6-3 over two legs.
The Senegalese international has enjoyed a sublime start to the season after his previous campaign was ended early by a knee injury, having racked up 13 goals and five assists in his maiden year on Merseyside.
Liverpool team-mate and summer signing Mohamed Salah, with two goals and two assists, was also in the running for the award but ultimately lost out, although he still took the club's internal Player of the Month gong.
They will hope to maintain their electric form in the Reds' first game back from the international break against Pep Guardiola's title-chasing Manchester City side this weekend.
For the official Premier League award, Mané also beat Manchester United trio Phil Jones, Romelu Lukaku and Henrikh Mkhitaryan - in spite of his five assists in three games - as well as Huddersfield Town goalkeeper Jonas Lössl and Chelsea striker Álvaro Morata.
On winning, he said: "I am very happy to accept this award because it means you are in a good way, but I am trying hard to improve. I want to say thanks to all of my teammates because without them I am nothing. I am happy with my start to the season. Everyone loves to score goals for their team, and it gives me more confidence."
Mané is the first Liverpool recipient of the monthly award since Luis Suárez and Steven Gerrard were named joint-winners in March 2014,
Reds boss Klopp won the Premier League's Manager of the Month last September and was also among the nominees for August 2017's prize, though was beaten by good friend David Wagner, of Huddersfield Town.
Can Mané fire Reds to glory this season?
Liverpool enjoyed a similarly blistering start to the season last year, topping the table in autumn after their front-three of Mané, Firmino and Philippe Coutinho helped them go 11 games unbeaten, scoring 28 goals in the process.
Injuries to a thin squad and Mané's absence due to the Africa Cup of Nations brought an early end to Liverpool's title challenge, however, as their threat to Chelsea fell apart at the seams in the New Year.
But a deeper squad this time around, though one still vulnerable in certain positions such as centre-back, and having Mané and Salah for the full season - dependent on injuries - bodes well for Klopp's team.
Whether their questionable defence will undermine their scintillating forward line remains to be seen, although their frailties at the back could potentially be exposed by the class of Manchester City at the Etihad Stadium on Saturday.
Certainly, Mané and Salah are two players who will test even the best of defences this season with their deadly blend of sublime technical qualities and athleticism, as well as the combination play, energy and speed of the front-three that they form alongside Firmino.
Mixed with their record against the top teams under Klopp, it appears Liverpool are a side to be wary of in both the Premier League and the Champions League as they look to make the next step under the German manager and claim some long-overdue silverware.