Iheanacho came out on top in an eight-man shortlist that included Andreas Christensen, Harry Kane, Jesse Lingard, Leandro Trossard, Luke Shaw, Illan Meslier and Riyad Mahrez.
The 24-year-old Nigerian international scored five goals in March, including his first ever top flight hattrick against Sheffield United.
Iheanacho is the fourth Nigerian to win the award after Jay-Jay Okocha, Peter Odemwingie and Odion Ighalo.
“I’m so pleased and honoured to win this award," he told Leicester's official website. It’s great to be recognised, but I couldn’t have done it without the support of my team-mates and the manager.
"I’m really enjoying playing at the minute and hopefully I can push on and help the team to finish as high as possible this season."
On the other hand, Tuchel scooped the managers’ prize after leading Chelsea to victories over Liverpool and Everton, and earning a draw away at Leeds United.
The German is still unbeaten as Blues boss and he won the award over fellow nominees Brendan Rodgers, Graham Potter and Ole Gunnar Solskjaer.
“I am really happy to have received this award and I believe it is a great achievement for everybody at the club who is involved in putting the team together to play each week," Tuchel told the Chelsea's official website.
"The award would not be possible if it wasn’t for the hard work of all my coaching staff and the wider support team who all push the team in the same direction, to achieve success.
"Lastly, I want to acknowledge the hard work of the players who have given me their maximum efforts and commitment since I arrived and we hope we can keep this strong run going until the very end of the season.”
