Both the company and the mining union said better safety standards were needed at the mine near Carletonville, southwest of Johannesburg. Company chairman Patrice Motsepe described the accident as a "wake up call to all of us".
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Production at the mine was halted shortly after the accident.
Sonjica, who visited a mine operated by AngloGold Ashanti this week where four workers died in a rock fall, ordered the Carletonville operation be shut down for six weeks.
"The mine must be closed until the shaft is repaired to give us certainty that the situation is safe," Sonjica told Reuters.
The miners were trapped when an air pipe broke off and hurtled down the shaft, damaging steelwork and severing an electrical cable carrying power to the main lift, said Graham Briggs, Harmony's acting chief executive.
The National Union of Mineworkers (NUM) blamed poor safety standards and Harmony's practice of mining 24 hours a day.
"We suspect negligence. Because of continuous operations there is no time to make adequate checks," NUM President Senzeni Zokwana told reporters.
Harmony dismissed the allegations of negligence, although Motsepe said additional measures were needed to protect workers.
"Our safety records both as a company and as a country leave much to be desired," he told reporters.
South African gold mines are the deepest in the world, and unions have often criticised companies for not doing enough to ensure workers' safety.
Gold mine operations have come under scrutiny over the past few months after a series of accidents. Companies are mining ever deeper to reach remaining seams and reap the benefits of a sharply higher world bullion price.
