Nduna Matshazi, a councillor for the opposition
Movement for Democratic Change, says he sent on a message about Mugabe "by mistake", the state-owned Chronicle reported this weekend.
Instead of sending it to a political chat group, Matshazi posted the message to a group of councillors for the rural district of Bubi in southern Zimbabwe.
The group's administrator, who is not being named, reported him to the police.
It's not clear exactly when Matshazi was arrested nor in which police station he is being held.
According to the Chronicle, which is published in Bulawayo, the message is a parody of the Lord's Prayer in the Bible. The administrator of the Whatsapp group says the prayer is "twisted to demean and attack the president."
Zimbabwe's insult laws were declared unconstitutional by the Constitutional Court in 2013 but justice minister Emmerson Mnangagwa (who is now vice president) said they were necessary and needed to stay in place.
Commenting on the arrest, a reader posted on the Bulawayo24 news site: "Do not trust open chat groups that are easily infiltrated."