Officers went to 1127 Gaillardia Way on a report of a stabbing at about 1:15 a.m., according to East Palo Alto police.
Arriving officers found a 43-year-old man suffering from knife wounds. The victim was treated at the scene by Menlo Park firefighters and then taken to Stanford University Medical Center.
He was reported to be in critical but stable condition, police said.
Police later arrested East Palo Alto resident David Cooks, who investigators believe had an argument with the victim then pulled out a knife and stabbed him.
Cooks was booked into San Mateo County Jail on charges of attempted murder and assault with a deadly weapon.
Anyone who might have witnessed the fight or has any information is asked to contact East Palo Alto police Detective Matafanua "Nua" Lualemaga at (650) 464-6838 or the anonymous tip line at (650) 851-8477.