Rayo's president Raul Martin Presa indicated he had reason to believe cables had been cut.
"Vandals have cut cables, we have tried to solve the problem as quickly as possible but told the stewards not to open the doors of the stadium. We will leave it to the police to find out who is responsible," said Presa.
The club confirmed as much in a statement.
"The match has been postponed for sabotage in the electrical system," the statement read.
There promptly followed a debate on when the match would eventually take place with Real wanting a late afternoon start on Monday but their hosts preferring an evening start."The date and kickoff time are to be confirmed," said Rayo.
Real Madrid's director of football, Miguel Pardeza, said: "We would prefer to have the match at 5pm as there is no guarantee that it will be repaired by 8pm and we have an already tight calendar. This is what our coach [Jose Mourinho] wants and although this isn't an ideal situation for anyone we prefer to play at 5pm."
But Rayo said they wanted an evening start out of "respect" for their fans – many of whom would still be at work in the event of an afternoon start.
Spanish television reported the match was likely to be rescheduled for 6pm GMT on Monday evening.
Fans were not allowed into the Estadio de Vallecas ground for security reasons Sunday for a match which had been due to start at 9.30pm local time (7:30 pm GMT).
Real were desperate for a win in the match having made a dismal start to the season to languish eight points behind leaders Barcelona after just one win in four games.
Local politician Cristina Cifuentes said an investigation will be opened to discover the full reason why the floodlights failed.
"We cannot jump to conclusions but we need to find the culprits if indeed this was a case of sabotage. Hopefully, we can now find a solution to have the match on Monday," she said.
Meanwhile the president of the Madrid football federation Vicente Temprado was worried about the damage the incident will have on the image of the Spanish game.
"This is very negative for football in our country that a game which was to be beamed around the world has not gone ahead – whether it is due to sabotage and a lack of security or not," he said.
Sources from television channel Canal Plus say cables were cut and the floodlight failure was not due to heavy rain in the area. – Sapa-AFP