An organ, windows and chairs were damaged after the youth stormed Rev Isaac Owusu-Bempah’s church in Accra.
Chief Imam Nuhu Sharabutu condemned the attack.
Self-styled Christian prophets have a huge following in Africa, and often predict major events, including the deaths of leading public figures.
In 2016, one of Africa’s most popular preachers, Nigerian TB Joshua, predicted during a church service that Hillary Clinton would defeat Donald Trump in the US presidential election.
Critics poked fun at him after Mr Trump won. The prophecy was later deleted from his Facebook page.
In a sermon on 31 December, Rev Owusu-Bempah made 18 prophecies for 2019, including the death of either Imam Sharabutu or Ghana’s Muslim Vice-President Mahamudu Bawumia.
Some Muslim youth asked the pastor to apologise to Imam Sharabutu, but he did not do so.
Armed with machetes, the group stormed a church of the pastor’s Glorious Word and Power Ministry on Wednesday.
The group streamed the attack live on Facebook, damaging property and razing to the ground a billboard with Rev Owusu-Bempah’s image.
Imam Sharabutu appealed for calm, saying those incensed by the prophecy should forgive the pastor, who is one of the most charismatic church leaders in Ghana.
Ghana is a mainly Christian country, with no history of religious conflict.
In its reaction to the attack, the Glorious Word and Power Ministry said: “Christians, let’s be strong and pray for the church.”