Needing a win to keep pace with leader Barcelona, Los Blancos slipped nine points adrift with just 13 games remaining of the Spanish league season.
Ronaldo had headed Real ahead on 33 minutes in controversial fashion and was then pulled down by Weligton to earn the penalty award.
The Portuguese star got up to take the spot kick, but saw his effort well saved to his left by home goalkeeper Carlos Kameni.
Zinedine Zidane's men were left to rue a rare miss by Ronaldo when Weligton crossed for Raul Albentosa to level 24 minutes from time.
It was the second time this season Malaga has shared the points with Real and the home side might have made it worse but for a fine Keylor Navas save from a looping header by Charles.
Ronaldo's opener was also disputed as he appeared to be in an offside position when he headed home a Toni Kroos free-kick.
It completed a difficult week for the three-time World Player of the Year, walking out of a press conference on Tuesday and seeing his great rival Barcelona's Lionel Messi score his 300th La Liga goal on the same day.
"It is obviously going to be difficult because we have dropped two points, but we won't give up," said Zidane.
Messi could have reached that landmark last Sunday, but instead of scoring from the penalty spot against Celta Vigo, he passed for Luis Suarez to complete his hat-trick.
Three victories in a week for Barcelona has taken the Catalan giant well clear of third-placed Real, while Atletico Madrid missed a chance to close up when held to a goalless draw by Villarreal in the Vicente Caldron later Sunday, now eight points adrift in second.
Real faces Atletico in the Madrid derby next weekend, but the two sides look set to be battling for the runner-up spot behind reigning champion Barca.
Man City thrashed
In the English FA Cup Sunday, Manchester City's unlikely hopes of a quadruple were ended in emphatic fashion by a 5-1 defeat to resurgent Chelsea under Guus Hiddink.
City, which faces a Champions League last 16 fixture in midweek and the English League Cup final with Liverpool next weekend, as well as campaigning for the English Premier League title, fielded a massively understrength side and paid the price,
In-form Diego Costa opened the scoring for Chelsea in the first half at Stamford Bridge before City's David Faupala leveled just before halftime.
The second half was one-way traffic as Willian, Gary Cahill and Eden Hazard scored. Oscar could even afford to see a penalty saved before Bertrand Traore completed the rout.
In another fifth round tie Sunday, Tottenham Hotspur's own hopes of the domestic double were ended by a shock 1-0 home defeat to fellow EPL side Crystal Palace.
Tottenham, second in the EPL and also still in the Europa League, exited through a Martin Kelly goal for the away side just before the break.
Dele Alli's first half shot for Spurs struck both posts and Harry Kane was twice brilliantly denied by away keeper Wayne Hennessey as Palace secured its first win at White Hart Lane since 1997.
West Ham joined fellow London sides Palace and Chelsea in the last eight with a 5-1 win at Blackburn in the early kickoff.