The call was echoed by the widow of one of the men, who died when Wood and others opened fire on them underground at the Aurora mine in Springs on August 9 this year.
One of the survivors of the shooting also called for Wood to be arrested and charged.
Yesterday morning Wood told talk-show host John Robbie on 702 Radio that he was solely responsible for the death of the four miners who died. He said the police should not charge the other people implicated and that he was the one who did the shooting.
The story of the killings was first reported in Sowetan on August 12.
NUM spokesperson Lesiba Seshoka said: "The necessary justice must take place. Police must arrest him now and haul him before the court as a matter of urgency."
Ronica Khoriyo, widow of Stanley Chitokwana, one of the dead illegal miners, said: "My husband is dead and we are suffering and they are still outside with their families. We are worried that because we are foreigners we will not get justice."
One of the survivors said Wood should be jailed like them.
"We were arrested and spent time in jail. Why are they still outside? Is it because they are white and we are black?"
He disputed that Wood was the only one with a gun and said his four accomplices had also been armed. He also denied that the illegal miners had guns.
"If we had guns why did Brad and his people not get hurt?" he asked.
Five people are expected to turn themselves in to the police on Monday. They will be charged with four counts of murder and six of attempted murder.
Police spokesperson Lungelo Dlamini remained adamant yesterday that the five people had a case to answer.
The police have refused to answer questions, including how many people were carrying guns the day they entered the shaft.
Seshoka accused the police and National Prosecuting Authority (NPA)of favouritism.
"If it were a normal citizen from a shanty township he would be in jail. We are happy that people will finally be charged but disappointed that it took so long.
"We hope this is not a public relations excise by the NPA so that they can be seen doing something and later drop the charges," he said.
Seshoka said the union would decide today whether to protest outside the court on Monday.
NPA spokesperson Mthunzi Mhaga said the five people were expected to appear in the Benoni magistrate's court on Monday.