The Serbian international has impressed at Craven Cottage since joining on loan from Newcastle United in January.
Mitrovic's strength and ability to hold the ball up have been matched by his finishing ability, with five goals in as many games in March.
The Cottagers beat Derby County, Sheffield United, Preston North End and Norwich City, as well as drawing against Queens Park Rangers.
"Aleksandar has shown strength, quality and perseverance to score important goals and assist his teammates too," Fulham boss Slavisa Jokanovic told the EFL website.
"I congratulate him for winning the award for March and I expect that he will continue to offer good performances to help the team in this crucial moment of the Championship season."
Mitrovic, meanwhile, said of his award: "I'm happy and proud, I'd like to thank my teammates for helping me to achieve this and I'm looking forward to the rest of the season.
"From the first minute here, I adapted really fast and my teammates have helped me a lot. I feel good to play every game on the pitch so I hope that we'll be able to fight for automatic promotion for the rest of the season.
"I needed to leave Newcastle because I needed game time and needed games in my legs and I was desperate to play football, to be on the pitch, to score goals.
"It works perfectly for me, I really enjoy it here, my family enjoy it and I hope it continues. The manager, obviously being Serbian too, helped me a lot and the style they play, the players they have, I like a lot."