Malema said many schools will not be ready and sending children back to school will expose them to the virus.
He also called on South Africans not to go to church.
On Tuesday, President Cyril Ramaphosa announced churches, synagogues, mosques and other recognised places of worship could resume services under Level 3, but limited to 50 people.
But the EFF says this is senseless and reckless.
"Despite publicly declaring that the government’s COVID-19 response will be guided by science, the president decided to bow to the selfish pressure of private white monopoly capital," Malema said.
"This is because if all our people were given payment holidays, guaranteed social grants, free water and electricity, then the only people who were losing were the capitalists because they were not making a profit.
"As a result, they sabotaged the lockdown," Malema said.
He also said private hospitals should be nationalised to enable people to access medical care and spoke out against the sale and purchase of alcohol during the lockdown.
"EFF must not be shaken when it pronounced itself on alcohol. Comrades lose votes on principle. This alcohol is going to compromise hospitals. There won’t be space for COVID-19 patients," Malema said.
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