Neilson led the Tynecastle side to an unbeaten month, with three wins and two draws, not conceding a goal in the process.
Hearts secured their return to the Premiership last month, winning the Championship for the second time since 2015.
Neilson has been at the helm for both promotions.
It is the second time he has won the award this season having first been Glen’s Manager of the Month for December when the team won all four league games.
“I’ve got to give praise to the players because they’ve earned this award as much as anyone else,” he said.
“To go through an entire month – five games – without conceding a single goal is tremendous, and at the other end of the pitch we scored 13 times so I really couldn’t have asked for anything more from them.
“We ended the season well and it’s now about resting before regrouping and starting the hard work all over again come June.”
Colin Matthews, CEO of Glen’s owner the Loch Lomond Group, said: “What a month April was for Hearts and Robbie Neilson. They are worthy winners of the Scottish Championship, and after the final performances of the season, it’s clear Robbie is deserving of the Glen’s Manager of the Month title. Congratulations to him and his squad, who I’m sure are all enjoying a well-earned break.”
Neilson revealed last month the club hit their season targets, reaching the points and goals aim, as they set their sights on a return to the Premiership.
“We told the players at the start of the season that if you hit 57 points you will win the league,” he said. “We did that on Friday night. A couple of weeks ago we were sitting on 50 and needed seven out of the next nine. We've managed to do it, which is great.
“We also spoke about goals scored. If you score more than 50, you will win the league. We've scored 63. The final one was that if you conceded less than 25 goals you would win the league. We've conceded 24.”