After toppling Spanish title challengers Sevilla in the last 16, the Foxes will now take on a team who have reached the Champions League final in two of the last three seasons.
Shakespeare said: “Facing a team who have reached the final in two of the last three seasons is a massive challenge but it’s just the kind of tie you expect in the quarter-finals of the Champions League.
“Atletico Madrid are a very good team with some fantastic individuals with experience in the competition, but we’ll be ready to give everything to progress.
“It will be a brilliant occasion for our supporters and for everyone at the club but, before the players can begin to think about these games, we have Premier League matches to come that are of huge significance to our season. They will be our sole focus.”
The Foxes, England’s sole representatives in the competition following the exit of Manchester City and Arsenal, will travel to the Spanish capital in the week beginning April 10, with the second match taking place the following week.
Two of Leicester’s four European ties prior to this season were against Atletico. The Spaniards came out on top of both, winning 3-1 on aggregate in the 1961/62 Cup Winners’ Cup before triumphing in both legs of a UEFA Cup tie in 1997 for a 4-1 aggregate victory.
The tie pits Leicester against one of the most consistent European teams of recent years.
As well as their two Champions League finals - they were beaten by city rivals Real both times, last year on penalties - Atletico also lost to Real in the quarter-finals in 2015 and won the Europa League in 2012.
Leicester are certainly the surprise name in this season’s last eight, and Atletico director and former defender Clemente Villaverde believes they cannot be underestimated.
He said: “In the previous tie and in the group stages they have shown they are a team to take account of, and the difficulty that we’re going to have is very high.”
Holders Real Madrid were handed a tough test in 2013 champions Bayern Munich and they will face former manager Carlo Ancelotti. Manchester City’s conquerers Monaco face Borussia Dortmund, while there is a repeat of the 2015 final, with Barcelona facing Juventus.
“It’s a fascinating challenge, against one of the most famous clubs in the world,” former Juve star Pavel Nedved said. “In my opinion, we have definitely grown. I believe that maybe this game is coming at the right moment for us.”
In the Europa League, Jose Mourinho got his wish for a short trip when Manchester United were paired with Anderlecht. The first leg will take place in Belgium on April 13, with the second match at Old Trafford a week later.
Anderlecht top the Belgian league by two points and are looking to win the title for the first time since 2014.
Juan Mata, the match-winner for United against Rostov on Thursday, has his sights firmly set on European silverware.
He said: ‘’It became a while ago very important for us. I still think we have the chance to get to the Champions League through the Premier League. I still think we can win a lot of games and get into the third or fourth positions.
Atletico Madrid v Leicester
Borussia Dortmund v Monaco
Bayern Munich v Real Madrid
Juventus v Barcelona
Ties to be played April 11/12 & 18/19
Anderlecht v Man Utd Celta Vigo v Genk Ajax v Schalke Lyon v Besiktas
Ties to be played April 13/20.