"Now they are showing that they are vicious and we will reciprocate because they have their properties here," Mugabe said in the state-run Herald newspaper.
"We are not without means to reciprocate," he said.
"It is violation of rules and regulations governing host countries of UN meetings."
Mugabe's wife Grace, his personal bodyguard, and four top officials were denied visas to attend to a meeting of the UN's International Telecommunications Union in Switzerland, causing the trip to be cancelled, according to state media.
The six are on the sanctions list imposed by the European Union and backed by Switzerland, which is not an EU member. Switzerland has not commented on the visas.
Swiss food giant Nestle operates a factory in Harare, which produces cereals and powdered milk for the local market.
Meanwhile, The Herald said Mugabe returned to Zimbabwe on Sunday from a private visit to Asia -- trips that have become monthly events amid reports that the 87-year-old leader is suffering from prostate cancer.
Mugabe has angrily denied reports that his health is worsening.
"You want to ask me about my health. As you can see, this Mugabe is fit," Mugabe told the paper.
According to the WikiLeaks whistleblower website, Mugabe has prostate cancer which has metastasized, and has been advised by doctors to cut on his activities.
The cable sent to Washington in 2008 said Reserve Bank governor Gideon Gono told the then-US ambassador, Jame McGee that Mugabe was told by doctors he had three to five years to live.