Dubai police chief Dahi Khalfan said sympathisers of the organisation, which has moved to the heart of public life in Egypt since President Hosni Mubarak was toppled last year, sought to weaken the UAE by defaming its institutions.
His remarks are likely to deepen a bitter public row between the Brotherhood and the UAE, which has in the past stripped citizenship from critics affiliated with Islamist organisations.
"Tweets by the Muslim Brothers have political goals," he said during a lecture to lawyers. "They belittle the symbols of the state and question the integrity of the judiciary... they want to stir the streets against us."
The UAE has avoided the kind of pro-democracy uprisings that shook other countries in the region. It has tolerated little dissent during the upheaval that resulted in the ouster of rulers in Tunisia, Egypt, Libya and Yemen.
It has moved swiftly against those voicing anti-government sentiments, including those who have taken to Twitter to fault the UAE leadership.
Last December, it revoked the citizenship of seven activists with ties to Islamist groups on the grounds that they posed a threat to national security.
Five other political activists were also convicted and then pardoned in 2011 on charges of insulting the UAE's leaders, inciting protests and disrupting public order.
Khalfan's row with the Brotherhood broke out in February, after the UAE decided not to renew residence permits of Syrians who had taken part in protests in Dubai against the rule of Syrian President Bashar al-Assad.
The move was criticised by an Egyptian cleric based in Qatar, which took him in during a crackdown against Egypt's Muslim Brotherhood in the 1960s. Qaradawi also denounced the move to pull citizenship from Emirati Islamists.
Khalfan lashed out at Qaradawi, threatening to arrest him if he set foot in Dubai, and on Tuesday said the Brotherhood was plotting to seize power in Gulf countries.
"Western intelligence services leaked to me a piece of information that says that between 2012 and 2016 the (Muslim Brotherhood) aims at creating governments in the Gulf that pay allegiance to them," he told reporters.
He said those who compare the UAE government to Egypt and Tunisia under autocratic rule should be prosecuted.
"They demand the ruler should be from amongst the people. Did we bring ours from Mars?" he said.