New Castle County police Officer John Weglarz Sr. says the shooting happened after an altercation Friday night at the First State Bowling Alley in Edgemoor.
He said it was not known what the altercation was about or who opened fire inside the building.
Authorities say four men and two women, all from Chester, Pa., had non-life threatening injuries.
Weglarz said the Chester High School Class of 2002 was having a reunion inside the bowling alley before the shooting.
Anyone with information can contact the New Castle County Police Department at 302-395-8110.