The Toffees have won all three of their top-flight games after beating Reading, Stoke and Manchester City to leave them just four points off fourth-placed Chelsea.
The Toffees secured maximum points with home victories over Reading, Manchester City and Stoke to lift the club to sixth in the table, four points off fourth-placed Chelsea, which currently occupies the league's final Champions League spot.
Everton's only blip in March was a 3-0 home defeat at the hands of Wigan in the FA Cup quarterfinal, but Moyes is delighted with his team’s league form at a crucial stage of the season and dedicated the award to his squad.
"It’s an award for all the players and how well they have done in March," Moyes told the club's official website. "The results they have had over the last month have been excellent, especially the games against Manchester City and Stoke City. It has kept us going and it is important you come into form at this time of year.
"Our form has never been too far away, and let’s hope we can keep that standard up right to the end of the season now."
Everton kicks off March with a crucial battle against third-place Tottenham at White Hart Lane on Sunday.