Long Beach teacher Kellye Taylor, 53, was slain about 1:30 p.m. PDT Friday in Orizaba Park while sitting in a folding chair as her 24 elementary school students played around her, KABC-TV, Los Angeles, reported.
The park is across the street from the Huntington Academy, a small private school owned by her mother where Taylor taught.
Steven Brown, 50, of Long Beach was arrested on suspicion of murder shortly afterward, the Long Beach Press-Telegram reported. He was being held on $1 million bail, KABC-TV said.
Police and witnesses said Taylor was stabbed in the neck.
About 100 friends, family members, former students and police officers attended a vigil for Taylor in the park Saturday, the Press-Telegram said.
"I don't know what I'm doing," Pamela Huffman, Taylor's younger sister and fellow teacher at Huntington Academy, told the newspaper. "I've never [done] this before.
"This is where my sister died."
City police Sgt. Aaron Eaton said the victim had a daughter and Brown was the father of her daughter's children.
Family members said Taylor had custody of the four grandchildren from her daughter's relationship with Brown, KABC-TV said.