Mugadza pastors from the Remnant Pentecostal Church based in the northern town of Kariba.
Mugadza had said in December that Mugabe would die on October 17 and urged him to pray hard if he wanted to avoid that fate.
The Southern African country has seen growing protests against its leader of 37 years, whom critics accuse of ruining the economy, but who nevertheless intends to seek re-election in 2018, when he will be 94 years old.
Mugadza was arrested in Harare on charges of undermining the authority of the president, but the charge was then changed to criminal nuisance, his lawyer Gift Mtisi said with Police spokesperson Charity Charamba confirmed the arrest.
Mugadza is not admitting to the charge against him, “as he is arguing that what he said was given to him by God during a prayer'', Mtisi said.
The pastor's arrest came as the ruling party prepares to throw a huge party to celebrate Mugabe's 93rd birthday on Feb. 21.
The pastor is expected to appear in court on Tuesday.
Meanwhile, Local Government Minister Savior Kasukuwere said the authorities would clamp down on priests raising alarm.
“These prophets are becoming reckless and careless, they need to be put on a leash,'' he said.