It is the height of the summer tourist season in Spain, and ETA has previously carried out attacks in vacation areas at this time of year in an effort to disrupt tourism.
The first blast occurred on a beach in Guadalmar at around 1 p.m. (7 a.m. EDT), and a second device exploded at a marina parking lot in Benalmadena Costa two hours later, the Interior Ministry said.
Both towns are around 340 miles south of Madrid in the Costa del Sol resort area on a stretch of coastline popular with foreign tourists, especially the British.
A caller who said he spoke in the name of ETA warned the fire department in the beach resort of Benalmadena that three bombs would explode, the ministry said.
The caller said bombs had been placed in Guadalmar, Benalmadena and on a highway linking Malaga to its international airport, a ministry spokeswoman told The Associated Press. She spoke on condition of anonymity in keeping with ministry rules.
Police had cleared the beach at Guadalmar, on the southwestern outskirts of Malaga, closed two roads and cleared more than 10,000 people in an orderly evacuation from the resort harbor at Benalmadena prior to the blast there, the spokeswoman said.
She said very little damage was caused by the bombs, but could not immediately give details.
Traffic around the port city of Malaga was gridlocked for hours following the warning and explosions.
In July, ETA set off a series of small bombs in Spain's northern beach resorts of Laredo and Noja, and one in Playa de la Carihuela, a short walk from Benalmadena's marina. One person was slightly injured in those bombings.
ETA has been fighting since 1968 for an independent Basque homeland in parts of northern Spain and southwestern France. The group has been blamed for killing more than 825 people.