Nine of the 28 people in the building, situated on one of the island's most popular beaches, are still missing, authorities said, with fears the death toll could still grow.
After working through the night, emergency workers "found a second dead person, a woman whose age has yet to be determined," local authorities said in a statement.
Three people, including a 28-year-old Italian man who suffered a broken arm, were rescued from the rubble late Thursday, with two requiring hospital treatment.
Four buildings located next to the collapsed block have been evacuated and dozens of families are living with relatives or staying in temporary accommodation.
Tenerife, the largest of Spain's Canary Islands off the northwest coast of Africa, is a popular destination for British holidaymakers and retirees.
It is also popular with German tourists.