Emergency services said eight people were detained in connection with the incidents that took place from 04:00 local time (0200GMT), sending people running in panic and leaving children in tears in different parts of the processions.
In a statement, the Cecop centre that oversees security during the processions in the southern Spanish city said those detained had variously "shouted", used metallic objects to make loud noise or made "wild gesticulations" to create panic in the thousands-strong crowds.
An AFP photographer present said she heard what sounded like a stampede of galloping animals, and then a mass of people pushed towards her.
Standing on the Isabel II bridge that goes over Seville's Guadalquivir River, she climbed onto a lamppost.
"There were children, women with prams," she said, adding some people rushed down steps towards the river, falling over themselves in panic.
"The first thing people think is that there is a terrorist attack."
An initial probe showed that there were three initial movements of panic, which sparked a "domino effect" in other parts of the city, Cecop said.
It added that the different incidents did not appear to be coordinated.
"These are isolated cases without any apparent connection that are similar to cases of vandalism and hooliganism," it said.
Cecop said three of those arrested were "common delinquents".
Some 17 people were taken to hospital for injuries and panic attacks, it said.
One of them was in intensive care in a serious condition, suffering from brain trauma.
A video posted on Spanish news site El Confidencial showed what looked like a post-panic scene, with people hanging onto bars on windows and the famed penitents, some of them with their hoods off, waiting anxiously as an onlooker on a balcony urged everyone to calm down.
The situation was later brought back under control and the processions continued.
Organised by religious brotherhoods and featuring huge floats of wooden sculptures of religious scenes accompanied by hooded penitents, the processions known as "La Madruga" are the high point of Easter Week festivities in Seville.
This morning's early incident mirrors a similar outbreak of panic in 2000 in Seville's Good Friday processions, which left 52 people injured.