An MDC official said Tsvangirai was given an emergency travel document on Sunday valid only for Swaziland and not for South Africa, which he needs to pass through.
"There is no way you can expect him to be in Swaziland when they are making it difficult for him," the MDC official said.
There were signs of failure before the summit kicked off.
"There have been developments in the past 24 hours that make it incredibly difficult for the MDC to have confidence in the current mediation process," the MDC said in a statement.
Their faith and hope in the current mediation process and its ability to deliver a solution to the people of Zimbabwe is now called into question," the MDC said in a statement.
Tsvangirai said on Sunday that he believed the parties would finalise a power-sharing deal at the meeting.
A power-sharing agreement, mediated by former South African president Thabo Mbeki, may be Zimbabwe's best hope for rescuing an economy where fuel and food are scarce and inflation stands at 231 million per cent.