The city put out a statement indicating that it was proud that the band chose Barcelona to launch the tour, though they're going to look into complaints and possibly take action against the concert promoters, Live Nation and Doctor Music.
Reports indicate that the band played nearly 2 hours past the 10 p.m. deadline and exceeded noise restrictions.
A Spanish paper, El Mundo, indicates that the fine could be more than $21,000.
The tour, which follows the release of U2's latest album, "No Line On The Horizon," includes concerts in 14 cities, culminating in Wales at the end of August. It's the group's first tour since The Vertigo tour in 2006.