A man has faced court charged over a series of random assaults at a Sefton Park shopping centre in Adelaide's inner-north.

The man allegedly assaulted several people yesterday as he walked through the Regency Plaza shopping centre on the corner of Regency Road and Main North Road about 1:15pm.

Police yesterday said the man "randomly attacked and punched at least six people".

A 56-year-old woman was taken to the Royal Adelaide Hospital with a concussion.

Police last night searched a Broadview house where they arrested a 20-year-old man just after 10:30pm.

He was charged with assault causing harm, aggravated assault and three counts of assault.

The man appeared in the Adelaide Magistrates Court where he did not apply for bail and was remanded in custody to face court again in June.

A police spokesperson said initial reports described a "serious and frightening" incident for people.

"Luckily we have arrested the person we believe responsible," the spokesperson said.

Police have appealed to witnesses or any other victims to contact them.