Malaga joined La Liga's traditional giants in the quarter-finals after overcoming Porto in the last 16, giving Spain the highest share of last-eight participants in the Champions League since England had four in the 2008-09 season.
The draw takes place at UEFA's headquarters in Nyon at 11am UK time on Friday and will be completely open, raising the prospect of bitter rivals Barca and Real being drawn together.
The failure of United against Real, combined with Arsenal's defeat to Bayern Munich over two legs and Celtic's loss to Juventus, means Britain is without a Champions League representative in the last eight for the first time in 17 years.
Reigning European champions Chelsea and Premier League champions Manchester City failed to even reach the round of 16.
Juventus' victory over Celtic means they have reached the quarter-finals for the first time in seven years, while Borussia Dortmund and Paris St Germain are making their first returns to this stage of competition for the first time in 15 and 18 years respectively.
Galatasaray's two-leg success against Schalke prevented Germany matching Spain by having three last-eight entrants, and keeps alive veteran forward Didier Drogba's dream of winning the Champions League two years in succession with different clubs.
The quarter-final first-leg ties will be played on April 2 and 3, with the return matches being played on April 9 and 10.
Europa League draw
While there is no English interest in the Champions League quarter-finals, the Premier League will be represented in the last eight of the Europa League after Tottenham Hotspur, Newcastle United and Chelsea all progressed on Thursday night.
The Europa League draw will also take place on Friday morning, with the first legs to be played on April 4 and the return matches taking place a week later.
Tottenham survived a massive scare before beating Inter Milan on away goals after a 4-1 defeat following extra time in Italy, with Emmanuel Adebayor's 96th-minute strike proving decisive.
Chelsea bounced back from a first-leg defeat to see off Steaua Bucharest thanks to a 3-1 victory at Stamford Bridge, with Fernando Torres netting the crucial third.
There was drama at St James' Park as Papiss Cisse scored the only goal of Newcastle's tie against Anzhi Makhachkala in the 90th minute to keep the Magpies' European dream alive.
The three English sides will be joined in the draw for the quarter-finals by Rubin Kazan, Basel, Benfica, Fenerbahce and Lazio.