Cook, who also won the March award, steered his side to 15 points from the month's eight games, scoring 17 goals in the process.
Wigan, who for the second month have secured an EFL awards double after Will Grigg won April's Player of the Month gong, have gone on to seal promotion into the Championship.
"Last month, when picking up March's Manager of the Month award, Paul spoke about being happier if he was sitting there with April's award," Sky Sports News pundit Don Goodman told the EFL website. "Well, now he's got his wish!
"After another taxing month with eight fixtures crammed into four weeks, Cook's Wigan side secured promotion with a thumping 4-0 win against Fleetwood in a run of games that highlight the depth and quality of the squad he has put together."