West Jordan Fire Chief Marc McElreath says the call for assistance was made at 9:00 p.m. Saturday.
More than 40 fire fighters had the fire contained within 30 minutes.
One unit is completely destroyed the other seven units have various levels of smoke damage.
The fire started in a kitchen where a 37-year-old man was reportedly deep frying food. Neighbors say he threw a towel over the flames, but the towel quickly ignited and helped the fire to grow out of control.
McElreath says the 37-year-old man threw his oxygen bottles outside and evacuated the building, but he burned his hands.
He and his wife were treated at the scene and are in good condition.
Neighbors say two dogs died in the fire.
Sean and Megan Christiansen live next door and were forced to evacuate the building because of smoke damage to their apartment unit.
They were called home early from a date to find their building fully engulfed. They were upset about the fire, but grateful no people were seriously hurt.