Meetings to gather views from the public were due to commence Saturday, in a process that would lead to a new constitution by September next year.
Currently the southern African country is under a 1979 constitution agreed at the Lancaster House talks in London and has been amended 19 times.
About US$36 million is needed to finance the process but government it is too broke to pursue the planned process.
A crisis meeting held late Thursday to resolve the issue failed to persuade the boycotting MPs to change their minds. The MDC has said that it is shocked by their decision.
According to them, this shows that Zanu PF is not committed to the Global Political Agreement that calls for the crafting of a new constitution.
The first major attempt to introduce a new constitution between 1999 and 2000 failed after the National Constitutional Assembly (NCA) and other civil society groupings successfully campaigned against a government sponsored draft.