Mugabe, the world's oldest president, is showing increasing signs of old age, but has refused to name his successor.
Zimbabwe goes to elections next year to vote for a president and lawmakers.
Chiwenga urged unfettered participation at the party's December special congress to choose new leaders.
"Members must go with equal opportunity to exercise their democratic rights," he said.
Chiwenga charged the ruling ZANU-PF party had been infiltrated by people who were seeking to destroy it from within.
"Known counter-revolutionaries... must be exposed and fished out," he said.
The purging in the party had plunged the country into a crisis, he said.
Chiwenga called on the ruling party officials to "stop reckless utterance... denigrating the military, which is causing alarm and despondency within the rank and file".
The army boss said the infighting in the party had impacted the country, which is reeling under an economic crisis.
"There is distress, trepidation and despondence within the nation," he said.
"As a result of the squabbling, there has been no meaningful development in the country for the past five years."
The crisis had resulted in "cash shortages and rising commodity prices," he said.
Zimbabwe in 2009 abandoned its own currency in favour of the US dollar due to hyperinflation.
But it started running out of those dollars and last year it introduced "bond notes", a parallel currency pegged to the US dollar.
The bond notes themselves are running short, forcing banks to ration cash withdrawals.