Two people on board the boat Alboran Cognac were rescued by a passing oil tanker. Scientists believe the whales may have attacked "playfully".
Spain's maritime rescue service said the two passengers reported feeling sudden impacts on the boat's hull and rudder, which caused water to leak into the boat.
Two people rescued from the yacht, which was left adrift and then sank, were rescued by a nearby oil tanker and taken to Gibraltar, alerting emergency services.
Whale strikes have become increasingly common in recent years in the Strait of Gibraltar, one of the world's busiest waterways through which about 300 ships pass daily, and off the Atlantic coast of Portugal and northwestern Spain.
Neuroscientist Lori Marino said: "If they really meant to do harm, they could easily do so. It is more likely that the apparent attacks "started as play behavior". We are talking about very intelligent beings and we know they are social learners."
Scientists think the endangered mammals "played" with the boats out of curiosity and imitative behavior rather than aggression.