The stabbing of the 77-year-old woman was reported at about 7:45 p.m. in the 1700 block of North Allen Avenue.
Los Angeles County sheriff's deputies found an ax handle - the blade was not attached - believed to be used to beat the grandmother. The knife was not immediately recovered.
"She was actually able to walk to a neighbor's porch and that neighbor summoned 911 for her," Lt. Cruz Solis said.
The suspect, later identified as Alex Touloudjian, "appeared not to be injured, however, he was covered in blood, but it appears to be the victim's blood," Solis added.
The elderly woman was taken to Huntington Memorial Hospital in serious, but stable condition.
Neighbor Dona Smith said the suspect kept to himself.
"Everybody keeps to themselves in the neighborhood here, but he's usually very quiet," Smith said.
The motive for the stabbing was not immediately known.