"We are receiving reports on other businesses that sympathised with the organisers of the stayaway and we are going to deal with them," he was quoted as saying by the Herald newspaper on Thursday.
"We want to identify those abetting the stayaway so that we can confront them and find what their motives and agendas are.
"We will actually invoke certain measures which will not be very comfortable with them. We cannot afford to stand by and watch people misbehaving."
The strike organised by the main Zimbabwe Congress of Trade Unions failed after the government warned protesters against participating in the strike, which it said was organised by the opposition Movement for Democratic Change (MDC).
The strike call came after Robert Mugabe's government launched a crackdown on the opposition which injured several people, including Morgan Tsvangirai, the leader of the MDC.