The News Tribune reports the damage was reported Friday. Several city workers were able to put at least half the headstones back in place.
City spokeswoman Carmen Palmer says Sumner police are pursuing several leads.
The cemetery opened in 1864.
Supervisor John Wells says the damage is worse than the last vandalism incident, in 2005. In that case, two teenage boys were convicted of causing as much as $170,000 in damage.
Wells didn't yet have a dollar estimate of the current damage.
Sumner is southeast of Tacoma.