Police are investigating the messages which are being sent through the main mobile phone operator Econet – which is deeply embarrassing for the company.
The SMS calls for Mugabe to be dumped as Zanu-PF president.
They also say the Zimbabwe Defence Forces will not recognize Vice President Joyce Mujuru.
Zanu-PF said this was the work of the enemy.
State TV compared the situation to the one in Iran where the opposition used text messages to rally supporters.
The storm erupted a day before Mugabe officially opens the Zanu-PF congress in front of more than 10 000 delegates.
Already there are signs tempers will be running high.
Mugabe has kept a tight grip on ZANU-PF since becoming party leader in the mid 1970s and spearheaded a guerrilla war against white minority rule. A personality cult has developed around him in the party, with some officials referring to him as the "second son of God" or the "supreme leader."
Last night, the Zanu PF Youth League and the Joint Operations Command, are alleged to have released mobile phone text messages from their base at Firstel Cellular offices in the Kopje Plaza claiming that the military is unprepared to salute Vice-President Mujuru and that provinces will ditch President Mugabe at the party’s congress.
Zanu-PF has tried to down-play the mobile phone messages as a "hoax" and the work of the "enemy".
In a Press Conference yesterday at the party’s headquarters in Harare, Zanu-PF Secretary for the Youth, Absalom Sikhosana said the message was not coming from the party.
"It (message) is coming from the enemy. That is how the enemy operates.
That is not our project. It is a project of the enemy intended to cause confusion and chaos during the congress. Our people must just ignore them. The Youth League is looking forward to the congress to help in building the country."
Commenting on the same matter, Zanu-PF’s Secretary for Education, Dr Sikhanyiso Ndlovu, dismissed the messages as a charade.
"The so-called threat to dump President Mugabe is a hoax and it shows political inexactitude as Zanu-PF is united under its leader," he said in a statement released in Harare yesterday.
Although Mugabe has flatly refused to discuss his retirement plans, analysts have said he is unlikely to contest the next presidential poll — expected in the next two years or in 2013 if the current unity government runs a full term. Ordinary members are calling on Mugabe to hand over power to someone younger.
One faction led by Defence Minister Emerson Mnangagwa is reportedly circulating documents at the congress spelling out "a get-out plan".
It is believed that the faction will run parallel structures in Zanu-PF with a long term plan to form a fully fledged break-away political party whose Congress is scheduled for September 2010.
A 200 page detailed document authored by former Information minister Jonathan Moyo details the "sources of funding, recruitment of members from Zanu-PF as well as the two MDC factions and external support".