Roofing collapsed in one building, and six units were reported to have been heavily damaged in the blaze, which firefighters had extinguished by 9:45 a.m.
One of those who called 911 was Kylee Decker, who lives in a unit in a building across from where the fire started.
She told The Salt Lake Tribune that she had just returned from taking her boyfriend to work when she noted an overpowering smell of burning plastic. When she looked outside, she saw the deck of the adjacent apartment on fire.
Decker said she ran across the street and, along with others, alerted residents to get out.
The Utah Red Cross said it was helping six families displaced by the flames, providing shelter, food and clothing as needed.
A cause for the fire had not been confirmed, but investigators are leaning toward an electrical problem, said Roy Fire Chief Jason Poulsen. The chief estimated the fire caused $450,000 to $500,000 in damage.
Tribune reporter Michael McFall contributed to this story.