Benitez, interim boss at Stamford Bridge, is the first Chelsea manager to win the award since Carlo Ancelotti in April 2011 after he oversaw an unbeaten month with three wins from four games.
The results have been enough to lift Chelsea into third place with four games remaining, but despite being in pole position to win UEFA Champions League football for the club, his popularity with fans remains well below 100 per cent.
The Blues beat Swansea City, Sunderland and Fulham and conceded a last-gasp equaliser to draw against Liverpool at Anfield.
Benitez has also helped to guide Chelsea to the final of the Europa League in Amsterdam later this month, where they will take on Portuguese side Benfica.
Van Persie, who won the player award in December, scored six goals for United in guiding them to their 13th Premier League title.
The highlight of his month was a first-half hat-trick in the 3-0 win over Aston Villa that confirmed them as English champions for the 20th time.