Two men who tried to come to their aid were also attacked, KPHO-TV reported.
Tony Garcia said another man used a fire extinguisher to try to drive the bees away Thursday evening and then handed it over to him after he was stung several times. Garcia was also stung.
But he said the two women were in far worse shape.
"They looked like that guy in the Guinness Book of World Records," Garcia said. "They were just covered head to toe -- no skin exposed, their faces weren't exposed, their clothes weren't exposed, the bees were in their hair -- they were just completely covered."
Killer bees or Africanized bees are descended from hybrids of African honeybees and European bees. The bees were crossed in Brazil in an effort to create a stronger bee.