Officers arrested a San Jose woman Saturday in connection with the homicide.
Police received a call from a home in the 1900 block of Johnston Avenue around 11 p.m. Friday. Arriving officers found two women who had apparently been physically attacked.
Kirk, who was from San Jose, was pronounced dead at the scene while the second woman, Sagal Mohamod Sadiq, was taken by ambulance to a hospital, where she was treated and released, police said.
Authorities later classified Sadiq as a suspect in the case, and she was booked into jail on suspicion of homicide.
Police said the relationship between Sadiq and Kirk, as well as the motive for the homicide, remains under investigation.
Investigators recovered the machete-type weapon believed to have been used in the murder.
This was the city's 39th homicide of 2011.
Anyone with information about this case is encouraged to call San Jose police Detective Sgt. Merlin Newton or Detective Jaime Jimenez at (408) 277-5283.
Those wishing to remain anonymous can call the Silicon Valley Crime Stoppers at (408) 947-STOP (7867) or visit svcrimestoppers.org.