Sinn Féin condemned the latest display as “racist”.
“This is an absolutely deplorable act following on previous hate displays at this location, said its Fermanagh and South Tyrone assembly member Colm Gildernew.
“The signage and effigy on the Moygashel bonfire is a clear hate crime.
“This is fuelled by hate and those that seek to bring division to our communities.”
Gildernew added: “The PSNI must investigate this as a matter of urgency to remove this disgraceful display.”
In a statement, the Democratic Unionist Party (DUP) said July bonfires “should be positive cultural celebrations”.
“The placing of flags, effigies or other items on bonfires is not part of that tradition and should not take place,” the party added.
The Social Democratic and Labour Party councillor for the area, Karol McQuade, said the mosque display was “vile, dangerous and deeply irresponsible”.
“There is no place in Moygashel, Mid Ulster or anywhere else for anti-Muslim hate, racism or the demonisation of an entire community,” he said.
“People should be able to live, worship, work and raise their families here without fear, intimidation or being used as targets for political stunts on a bonfire.
“Those responsible need to take this down immediately, and this should be treated with the seriousness it deserves by the authorities.”
