Officials had previously ordered matches to be played behind closed doors for a two-week spell.
La Liga and Madrid took action Thursday after a member of the club's basketball team tested positive for COVID-19. Madrid's football and basketball teams use the same facilities.
La Liga said the decision to suspend play will be re-evaluated in two weeks.
Madrid's upcoming Champions League match against Manchester City is also expected to be postponed, according to The Guardian's Sid Lowe. Los Blancos are scheduled to play the second leg of their last-16 tie in Manchester on Tuesday.
Madrid had been due to face Eibar on Friday in the first of the weekend's La Liga fixtures. It's unclear when the games will be rescheduled.
No player from the Spanish top flight has been reported to have the virus. However, the league said it's wary that possible cases may arise.
UEFA allowed Champions League matches to go ahead behind closed doors this week. Valencia lost 4-3 to Atalanta in front of empty stands at the Estadio Mestalla on Tuesday. Paris Saint-Germain also hosted Borussia Dortmund without spectators at the Parc des Princes on Wednesday.
Meanwhile, Europa League matches between Sevilla and Roma and Getafe and Inter have been moved to a later date. Roma's plane wasn't given permission to land in Spain amid concerns about the coronavirus outbreak in Italy.
All sporting events on the peninsula, including Serie A matches, have been postponed until April 3 in an attempt to control the spread of the virus.
Juventus defender Daniele Rugani became the first player in the Italian top flight to contract COVID-19. More than 1,000 people have died from the new virus in Italy.
Eighty-four people have died from COVID-19 in Spain and more than 2,000 have been infected.