Union deputy general secretary Gideon du Plessis said the men were assaulted outside the mine's premises as they reported for duty on Monday morning.
"One of our members sustained stab wounds and another sustained burn wounds. The third member has a fractured jawbone." Du Plessis said.
Solidarity called on the police and the mine to take action. It had sent a letter to Lonmin, demanding protection of workers.
"If the employer fails to meet this demand, Solidarity will withdraw its members from the workplace for safety reasons," said Du Plessis.
Four people have been killed in the violence at the mine in the past four days.
A man was found gunned down on the mine's premises on Monday, and another died in hospital after being hacked at the mine with a panga on Sunday.
Two security guards died on Saturday when their car was set alight. Four other workers were shot and wounded on Friday and Saturday. Eight vehicles were torched on the mine property on Sunday.
Violence at the Lonmin Marikana mine has been linked to clashes between members of the National Union of Mineworkers (NUM) and the Association of Mineworkers and Construction Union (AMCU), which are reportedly fighting for control of local mines.
Police spokesman Brigadier Thulani Ngubane said no arrests had been made on Monday.
In February, the two unions also clashed over membership at Impala Platinum's mines in Rustenburg.
Meanwhile, Cosatu's North West branch on Monday called on a rival labour union to put an end to the violence at Lonmin's mine in Marikana.
Provincial secretary Solly Phetoe said the Association of Mineworkers and Construction Union (Amcu) should give miners freedom to choose a union.
"Cosatu wants to remind Amcu that the Constitution of our country allows workers a freedom of association," Phetoe said.
"That right has been extended in the Labour Relations Act which give workers the rights and powers to form their unions, and not to be forced to join some fly-by night unions."
Violence at the mine had been linked to clashes between members of the Cosatu-affiliated National Union of Mineworkers and Amcu, which were reportedly fighting for control of local mines.