Social media videos shot in the Plaza Major showed injured fans and officers in body armour wielding batons.
BBC journalist Phil Mackie confirmed police used baton charges to clear parts of the square.
Earlier, Spanish police said eight Leicester fans were arrested for “causing a mess” on Tuesday night.
Footage posted online showed a group of officers being targeted with missiles and fans chanting
“Gibraltar is ours” in the Plaza Major, where Leicester’s fans were told they could congregate.
A witness told BBC 5 live: “There were a couple of people who probably antagonised the police, but then they took it out all these people here.
“There were people with children, they came in with batons and there was a 70-year-old man and the kids [in the way] .”
Owynn Palmer-Atkin, reporting for BBC Radio Leicester, said: “There was a couple of flares that went off – blue smoke, then a bang, and that is when you heard the tone of the chanting change.
“The noise of the crowd seem to quieten and then become more of a panic.
“There was another bang and that is when the riot vans started charging across the square. I find it incredible a police van would travel that fast in a crowded square.”
BBC presenter Gary Lineker, a Leicester City fan and former Foxes player, tweeted: “Just saw the footage of some Leicester fans behaving despicably in Madrid. The few idiots ruin it for the decent majority. Sickening.”