Julius Malema is being investigated for inciting violence during the strike at Lonmin's Marikana mine, in North West, the Hawks say.
"We are investigating charges that have been brought by Solidarity," spokesperson McIntosh Polela said.
"They have opened a case of incitement and intimidation. It has been referred to us and we are currently gathering information to help us with our investigation."
On Sunday, it was a month since police opened fire on a group of protesters on a hill near the Marikana platinum mine, killing 34 mineworkers and wounding 78.
Another 10 people, among them two policemen and two security guards, died the preceding week. A 45th person, a union shopsteward, was found dead weeks after the shooting.
Workers are demanding that their wages be increased to R12 500 a month.
Malema arrived at Marikana two days after the shootings took place.
He told the crowd that President Jacob Zuma and Police Minister Nathi Mthethwa must resign following the shooting.
"President Zuma decided over the massacre of our people. He must step down."
He said Mthethwa should also resign because the police shot people under his command.
"He must resign because he failed in executing his duties."
Malema told the crowd that the police were supposed to protect them and not kill them.
"It has never happened before that so many people were killed in a single day and it became normal," he said.
Malema, who pledged his support for the striking mineworkers urged them not to retreat and to stand firm on their demand for a R12 500 salary.
He said the reason the police shot at the people was because they were protecting the interest of ANC National Executive Committee (NEC) member, Cyril Ramaphosa, who he said owned shares in Lonmin.
"Lonmin had a high political connection that is why our people were killed. They were killed to protect the shares of Cyril Ramaphosa," he said.
He told the gathering that it was amazing that Ramaphosa was able to buy a buffalo for R18-million, but could not pay them the R12 500 they were demanding.
He called on the mineworkers to form a militant union that would represent their interests.
He said that the National Union of Mineworkers (NUM) was no longer a union that represented the interests of the workers, but was more interested in making money.
"NUM is not a union, it's a company. They hold shares in mining companies, that is why, when there are problems in the mines, they are the first to sell out the workers." – Sapa.