The suspect was identified as Jabulani Mdunge, 38.
Magaqa, who was a former Umzimkhulu ward councillor, succumbed to his injuries in a Durban hospital on September 4 after he was shot in a drive-by shooting.
Magaqa's family believes his killers could be found in ANC party ranks, while his friend, Les Stuta, said he was killed because he was on the brink of exposing corruption linked to a community hall.
The Hawks are reportedly close to arresting a second suspect in the killing.
The breakthrough in the case comes after Police Minister Fikile Mbalula's visit to Umzimkhulu last Thursday, when he attended a memorial service and paid his respects at the Magaqa home.
He promised to have Magaqa's killers - as well as those responsible for political killings in the province - caught and dealt with.
"We catch them and they will sh*t themselves. When we catch them we won't let go until they sh*t themselves because if we allow this to continue there will be anarchy.
"I'm the police minister and I cannot lead cops and criminals," the police minister said.