The order comes two days after Buddhist monks led a crowd trying to storm the mosque in the central town of Dambulla.
Prime Minister DM Jayaratne says the mosque has simply been ordered to relocate to another part of the area.
But the incident has angered senior Muslim politicians.
Buddhist monks in central Sri Lanka had threatened to demolish the mosque next week if the authorities did not act first. A special meeting to discuss the issue appears to have been convened on Sunday, and this statement was produced.
The statement listed four prominent Muslims as present at Sunday’s meeting agreeing to relocate the mosque – but according to a weekly Muslim paper, three of them say they were not there.
Cabinet minister AHM Fowzie told the BBC he had not been to such a gathering. He added that it would be acceptable to request such a relocation but not to order it.
Another politician of the governing party, Azath Sally, said that even if the mosque were illegal, people opposed to it should not “act like thugs”.
“Do Tamils and Muslims not have a right to live in this country now?” he added.
Our correspondent says that whereas Sri Lanka’s Muslim community normally shies away from confrontations with the government, this incident has angered some senior Muslims and prompted them to speak out.
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