Tsvangirai’s Movement for Democratic Change (MDC) party formed a fragile coalition government with Mugabe’s ZANU-PF in February, raising hopes this would end a long-running political crisis and a decade of economic ruin.
Mugabe chairs cabinet meetings held every Tuesday and Tsvangirai presides in Mugabe’s absence.
Thokozani Khupe, deputy prime minister, said Mugabe was due to leave for Libya later on Monday and Tsvangirai, who has returned from a tour of European countries and the United States, would have presided over the meeting on Tuesday.
Khupe told journalists the decision was one of several unilateral decisions made by Mugabe, disregarding a political agreement reached last year.
"The decision seeks to deny the recognition of the prime minister as chair of cabinet when the president is away. This reflects unilateralism, disrespect, contempt and the refusal to recognise reality," Khupe said.
ZANU-PF officials were not immediately available for comment.
During his overseas tour, Tsvangirai sought to play down disagreements with Mugabe, saying he had a working relationship with the veteran 85-year-old leader.
But Khupe said Mugabe continued to violate the political agreement, including failing to swear-in senior MDC official Roy Bennett as deputy agriculture minister, while the national security council had never met because "a few elite securocrats do not recognise the authority of the new order".
She said ZANU-PF was frustrating media reforms while MDC legislators and civil society members continued to be victimised and arrested.
The MDC has already asked the regional Southern African Development Community to mediate in a dispute over the appointment of the central bank governor and attorney general.
"For a long time we have remained the polite and subservient upholders of the GPA (global political agreement)," said Khupe.
"Whilst we remain fundamentally committed to the GPA in the interests of our people, it is our constitutional right to consider disengagement," she said, without elaborating.
Tsvangirai has said his party would not quit the unity government and told Reuters on Saturday that Western pressure for Mugabe’s removal could lead to chaos in Zimbabwe.
Western donors, crucial for Zimbabwe’s recovery from a 10-year economic crisis, have said their aid will only flow to the southern African country when reforms are implemented.