The Issaquah-Wash.-based company said the federal Centers for Disease Control and Prevention reported 25 cases of people sickened by E. coli O157:H7 in those states during that time.
In its own statement, the U.S. Food and Drug Administration said the illnesses include 11 in Arizona, eight in Colorado, three in New Mexico, two in Nevada and one in California.
No deaths have been reported, but nine people were sick enough to be hospitalized, the FDA said. One possible case of hemolytic uremic syndrome, a type of kidney failure, was reported, the agency said.
Symptoms of E. coli infection include bloody diarrhea, abdominal cramps, dehydration and in severe cases, kidney failure. The FDA advised anyone experiencing those symptoms to contact a health care provider.
The cheese is manufactured by Bravo Farms of Traver, Calif., south of Fresno. The FDA said it and California state officials have begun an investigation at Bravo Farms.
Bravo Farms did not immediately reply Thursday night to an Associated Press e-mail seeking comment.
Consumers should return any remaining Bravo Farms Gouda to Costco for a refund, Costco Assistant Vice President Craig Wilson said. Costco has voluntarily removed the cheese from its stores and used purchase records to notify other consumers.
The FDA, CDC and Costco are working together on the investigation.
The first results of Costco's own testing were expected Friday, Wilson said in a telephone interview.