Mohamed Boudarbala, 36, was found dead Friday in his cell in a new prison in the southern town of Archidona currently used as a so-called CIE -- a centre where migrants are held pending asylum claims after they arrive in Spain.
Police said Tuesday an autopsy revealed he "hanged himself with a sheet".
At a press conference in the southern city of Malaga organised by the Citizens' Platform Against the CIE of Archidona, his brother Ahmed Boudarbala denied Mohamed was suicidal.
"I was in contact with my brother every day, we called each other, he complained about the food, the cold, but he didn't complain about life," he told reporters in Arabic comments translated into Spanish.
"He was sporty, young, very happy and very positive.
"He died in murky circumstances."
Ahmed alleged that his brother had been beaten by police -- along with others -- inside the centre hours before his death.
Relatives of other people in the centre have also made claims of police brutality, according to the platform.
Asked whether there had been unrest before Boudarbala's death, a police spokesman said he did not know.
Spain's interior ministry did not respond to emailed questions over claims of police brutality.
Daniel Machuca, spokesman for the citizens' platform, said relatives of those inside had described living conditions as "terrible," with no hot water for instance.
He added they claimed riot police had charged at those detained following protests over living conditions.
Police said Friday they had opened an investigation into Boudarbala's death.
His brother Ahmed and the platform called for authorities to stop deporting migrants from the jail back to their homeland, as these could be potential witnesses in the probe.
Spanish authorities said last year they had to use the jail as a CIE due to lack of space in other centres, adding however the prison had better facilities, including new showers, heating, beds and sports areas.
According to the International Organization for Migration, migrant arrivals by sea to Spain tripled in 2017 on the previous year, with some 21,500 people arriving.
At least 223 people died or disappeared while trying to reach Spain by boat.