The first leg of the two games, aggregate goals series is set for March 18 at Olympic Stadium with the second leg in Alajuela, Costa Rica on a date yet to be confirmed between April 7 and April 9.
The Impact reached the semifinals for the first time thanks to a dramatic goal by rookie Cameron Porter in the dying seconds of their quarter-final on Tuesday night. It gave them a 1-1 tie in the game against Pachuca of Mexico and a series win on the away goals rule.
Coach Frank Klopas said Alajeulense is a very different opponent.
"Pachuca was very direct, with a lot of pace out wide," Klopas said Thursday. "The Costa Ricans are more of a team that builds up play.
"They possess the ball. It's a different opponent with different dynamics but we'll be ready for them. I know the guys are looking forward to it, and I know this place will be packed."
A crowd of 38,104 turned out for the Pachuca match. Tickets go on sale Friday for the semifinal.
Klopas will likely miss the semi. He was ejected after Porter scored for going onto the field. He had been warned earlier to stay in the coaches' box near the team bench.
"The fourth official told me that no matter what happens, whether it's me or someone else doing it, I was going to get ejected," said Klopas. "In the 95th minute, I think you could have kicked everyone off because we all ran on the field.
"It was all those emotions, the tension of the game, and on the last play of the game, to have a goal like that is once in a lifetime. I'll be an old man and I'll still be thinking about it."
Alajuelense defeated DC United 6-4 on aggregate in their quarter-final. Montreal is the last MLS club left in the competition.