The readings need to be evaluated to see if they exceeded permitted levels, city hall spokesperson Inmaculada Sanz said in a press conference on Thursday. She said the authorities had received 25 complaints after Wednesday's gig.
She said city hall was already preparing fines for promoters of previous concerts that have been judged to have exceeded noise limits.
Real Madrid declined to comment. Madrid's municipal police referred requests for comment to city hall. Sanz did not give the decibel reading at the press conference.
Swift's promoter for her Madrid concerts Lastur Bookin SL did not immediately respond to a message seeking comment.
Her concert, attended by tens of thousands of "Swifties", marked the first performance by a global megastar at the stadium that has been adapted to meet President Florentino Perez's vision to expand the club's income beyond football so Real Madrid can compete financially with English clubs in the lucrative Premier League.
The 900 million-euro ($978-million) revamp included a roof and new state-of-the-art retractable pitch allowing the use of the venue for events, making it "an epicentre of the entertainment world", Perez said in November.
But the plan is running up against local anger at the noise levels, with residents saying they will seek legal recourse to block future events.
"We have no choice but to take legal action," said Enrique Martinez de Azagra, president of the Association of People Affected by the Bernabeu.
During Wednesday's concert, experts contracted by the association took their own decibel counts which can be used as evidence in a case. The experts recorded readings of 80 decibels, far above the 53 permitted by city authorities for a concert venue, Martinez de Azagra said.
Swift's concerts on Wednesday and Thursday will help swell Real Madrid's coffers as it pays off 1.2 billion euros of outstanding loans and structured deals.
A club source told Reuters in 2021 the refurbishment would boost annual stadium revenues to 400 million euros from 150 million.
