Carlo Ancelotti's men were hoping to extend their winning run in the top flight to eight matches but failed to make the most of their dominance at the Santiago Bernabeu.
Their first-half performance was especially disappointing as Madrid arguably only created one clear-cut opportunity.
Los Blancos were more dangerous after the interval but still could not break the deadlock and nearly saw Madrid youth product Alvaro Negredo steal a late winner for the 19th-placed visitor.
Madrid showed promise early on as Karim Benzema released Vinicius Junior into the left side of the area only for his eventual shot to be deflected behind by Juan Cala.
Otherwise, Los Blancos did not pose much of a threat to Jeremias Ledesma's goal until the second half, when he was forced into a fine save by Eden Hazard's delicate header.
Vinicius was the next to test Ledesma just before the hour, cutting inside Carlos Akapo and drilling straight at the goalkeeper from 16 yards.
Thibaut Courtois was helpless at the other end 15 minutes from time as Cadiz countered and saw Negredo shoot towards the bottom-right corner, only for the effort to be dragged agonisingly wide.
Madrid subsequently piled the pressure on, with Benzema going close twice and Toni Kroos having a strike blocked, but Cadiz left the capital with at least a point for the second successive season.