Mr Tsvangirai had planned to address a major MDC rally in Bulawayo
Zimbabwe's opposition has alleged the military is plotting to assassinate its presidential candidate using snipers.
Movement for Democratic Change (MDC) leader Morgan Tsvangirai postponed a return to Zimbabwe at the weekend.
He was due to start his campaign to defeat Robert Mugabe in a presidential election run-off on 27 June.
"We know there are 18 snipers, and the military intelligence directorate is in charge of this," MDC Secretary General Tendai Biti told reporters in Nairobi.
"Mugabe's military intelligence has compiled a list of 36 to 40 people to be assassinated. Top of the list are our leader Morgan Tsvangirai, myself and our spokesman Nelson Chamisa," Mr Biti said.
The US ambassador to Zimbabwe has warned that post-election violence makes a fair second round run-off vote impossible.
Opposition and human rights groups have said hundreds of opposition supporters have been beaten up and at least 30 killed since the first round on 29 March.
The ruling party denies supporting violence and says the West is trying to demonise Zimbabwe.
According to official results, Mr Tsvangirai won the presidential poll, but not by enough to avoid a run-off with President Mugabe.
MDC supporters have been beaten in rural areas
He has insisted he did pass the 50% threshold and so should have been declared the outright winner.
Mr Tsvangirai has spent more than a month outside Zimbabwe since then trying to drum up international support.
At the weekend, he had been due to speak to newly-elected members of parliament from his party, who will form a majority for the first time since independence.
The MDC leader had also planned to address a major rally in Zimbabwe's second city, Bulawayo, on Sunday.
Last year, Mr Tsvangirai was treated in hospital after being assaulted by police.
Are you in Zimbabwe? Have you been affected by any of the issues in this story? Send us your comments using the form below.
The BBC may edit your comments and not all emails will be published. Your comments may be published on any BBC media worldwide.