The forward was sent off for reacting to a shove by Carlos Gurpegi and then a confrontation with Ander Iturraspe in the 75th minute, although he appeared to be more sinned against than sinner.
Only a minute earlier Athletic had scored a brilliant equaliser through substitute Ibai with only his second touch after coming on, firing in a bouncing ball from the edge of the area.
Madrid held on for a point, having gone ahead after 65 minutes through striker Jese on his first league start, but the loss of Ronaldo now through suspension, for a possible three games, could well have an impact in the Primera Division title race.
These two dropped points left them three points behind city rivals Atletico and level with Barcelona.
After a bright opening from Madrid, Athletic wasted two golden chances to take a first-half lead.
First Aritz Aduriz, making a run inside from the right, raced on to a through-ball and poked it past a defender to give himself a clear sight of goal - but could only bend his left-footed shot wide of the left post.
Iker Muniain missed an even better opening shortly afterwards. An expertly-measured low ball in from the right found him at the back post, but the forward appeared to be in two minds over whether to take a touch or shoot first time and only succeeded in knocking the ball behind for a goal-kick.
Madrid's big guns were struggling to get into the match, with Ronaldo largely anonymous in the opening 45 minutes.
The visitors, missing world record signing Gareth Bale through injury, started with far more urgency after the break, though, Luka Modric bringing a diving save out of Gorka Iraizoz with a curling shot from the right.
Karim Benzema then fired in an effort which Iraizoz parried as Madrid upped the tempo.
And the Frenchman was involved as Madrid took the lead after 65 minutes, playing Ronaldo in down the left of the area, and the Portugal forward laid the ball across the goal for Jese, sliding in, to stab it home.
Athletic brought on Ibai for Muniain after 73 minutes and the new man made an instant impact with a superb goal less than a minute later.
With his side having a free-kick as he came on, Ibai lofted the set-piece into the area. It was headed clear, but he met the loose bouncing ball on the edge of the area with a stunning strike which flew in off the far post.
And things got worse for Madrid as Ronaldo saw red after reacting to a shove by Gurpegi and then clashing with Iturraspe, although he could count himself hard done by.
Ronaldo was pushed by Gurpegi after appealing for a handball in the area and responded by brushing his hand into the Athletic man's face.
Gurpegi tumbled to the turf in an apparent attempt to get his opponent sent off and Ronaldo was confronted by Iturraspe, who clearly pushed his head into the Madrid player's face. Ronaldo left his head there and then raised his hand to lightly push Iturraspe away, but his actions were hardly aggressive.
But, as the melee died down, Iturraspe was shown a yellow and Ronaldo a seemingly harsh red.
Ibai then brought a fine save out of Diego Lopez, who also kept out a powerful Aduriz header, but Athletic were unable to find a winner against the 10 men.