Photos have been circulated in social media of the embassy after the fire was put out, arabi21 website reported.
A much-condemned deal was recently signed between Israel and the United Arab Emirates (UAE). The deal was announced on Thursday.
US President Donald Trump, who apparently helped broker the deal, has attempted to paint it as a big breakthrough.
The move has drawn strong criticism from many Islamic countries and regional organizations.
The UAE is now the third Arab country, after Egypt and Jordan, to normalize with Israel. Abu Dhabi was already believed to have clandestine relations with Tel Aviv.