The body of 65-year-old Ms Martorell, who the police had previously been unable to identify, was discovered in a flat following a fire in Harvey Street at about 4.15 am on Saturday.
The 28-year-old man, who was arrested on Monday, has been taken to the Serious Crime Suite at Musgrave Police Station for questioning, said the PSNI.
Police said Ms Martorell had sustained multiple injuries from an unspecified type of weapon during a “horrific attack” before a ground floor flat was set on fire.
Her body was found when firefighters attended the scene.
There was an increased police presence in Derry at the weekend following the incident.
In a statement earlier on Monday, the police said they were aware of “online speculation”, which they said was “extremely unhelpful and deeply distressing to Ms Martorell’s family”.
Detectives had earlier appealed to speak to a white man, aged in his 30s, who was seen in the area.
Det Ch Insp Kelly said detectives were working at full pace to establish exactly what happened to her
“My thoughts at this time are first and foremost with Ms Elias’ family and friends in Spain, who are left trying to come to terms with their loss,” Det Ch Insp Kelly said.