A caller claiming to represent Basque separatists, who have targeted Spain's tourist industry before, phoned a warning before the devices went off.
The injuries were caused by flying glass when a bin exploded near a yacht club in Sanxenxo in the Galicia region.
A second bomb near a marina in Baiona, also in Galicia, caused no injuries.
A caller claiming to represent the Basque separatist group Eta had phoned a Basque newspaper to say explosions were imminent in the two towns.
"Whoever is behind these attempts, the full force of the law in going to come down on them," he said.
Four small bombs exploded at holiday resorts on the country's northern coast earlier this month.
For more than three decades, Eta has waged a bloody campaign for independence for seven regions in northern Spain and south-west France, leaving at least 800 people dead.
It has been declared a terrorist organisation both by the EU and the US.