Ancelotti guided Everton to three wins out of three in the month of September to take the Toffees top of the table.
The 61-year-old Italian came out on top in a four-man shortlist that included Aston Villa manager Dean Smith, Jurgen Klopp and Brendan Rodgers.
This is the fifth time Ancelotti has won the Premier League’s manager of the month award, having also done so four times during his previous spell in England as Chelsea manager.
"It's a great achievement. I have to share with my team and my players," Ancelotti said, with his side hosting Merseyside rivals and champions Liverpool after the international break.
"We've started really well and we hope to continue it and to win this award again."
Calvert-Lewin wins the award for the first time a day after making a goalscoring debut for England in an international friendly with Wales at Wembley.
The 23-year-old is the joint top scorer in the top flight with six goals, including a hattrick against West Bromwich Albion on matchday 2.
Calvert-Lewin was shortlisted for the award alongside teammate James Rodriguez, Harry Kane, Tariq Lamptey, Patrick Bamford, Sadio Mane, Timothy Castagne and Jamie Vardy.
“A great start to the season. Thank you to my team mates and the people that voted,” Calvert-Lewin tweeted after being announced as the winner.
