"By denying the first lady the visa, the Swiss were trying to put apart what God had tied," Mugabe's spokesman George Charamba told AFP.
Switzerland also denied visas to the foreign minister, the communications minister, the director general in the presidency, Mugabe's personal bodyguard, and Charamba, the spokesman said.
Mugabe was due to travel to Switzerland with his wife and the officials to attend a meeting of the UN's International Telecommunications Union underway in Geneva.
Mugabe and his inner circle were slapped with travel bans by the European Union in the aftermath of the 2002 presidential poll, which western observers said were rigged to hand Mugabe victory.
Although Switzerland is not an EU member, it has signed onto the travel ban. Normally the ban is waived for UN events.
The Swiss embassy in Harare refused to comment on the matter.
State media reported that government has lodged a complaint with the United Nations and Swiss authorities over the issue.
"We noted that this was a highly regrettable decision which was a clear violation of the United Nations headquarters host agreement and Zimbabwe's sovereign right to determine the composition of its delegation," the state-run Herald newspaper quoted an unnamed government official as saying.