The painting at the mosque located a few metres away from the University of Botswana, exalted Jesus Christ and Christianity.
Further, the authors stated that Botswana is a Christian society and called upon all Muslims to submit to the Christian faith.
“I doubt any sane Christian would do such a thing, it must be someone who wants to incite conflict between the two,” said Mr Boikanyo Sethibe of Gaborone.
His elder brother, Kagisano, suspects it could be the work of Satanists.
“I suspect it could be Satanists – they just want to see Christians and Muslims fighting. People should not read too much into this, otherwise we will end up fighting for no reason,” Mr Kagisano told the Africa Review.
The chairman of the Muslim Association in Botswana, Mr Satar Dada, expressed regret at the writings, adding that the organisation would not want to comment further until police investigations were complete.
“It is regrettable that someone would go out of his way to offend a sacred place of worship through such disturbing statements,” Mr Dada told a local Sunday paper.
Botswana has never had Muslim-Christian clashes in the past.
The southern African country is predominantly Christian with a few mosques dotted around the capital Gaborone.