Those living in the country could also face jail, and foreigners deportation.
The new law was brought to light when the UAE's supreme court ordered the retrial of a man fined $800 for the offence, arguing the fine was too lenient.
The man was convicted of swearing at a colleague using the smartphone instant messaging app.
The exact words used by the defendant were not revealed by the court, which simply said that they were "insulting", according to 7Days UAE.
The claimant told police the defendant also threatened to harm him, though the defendant was cleared of the charge.
The case against the man was brought under a cyber crime law introduced in the UAE in October last year that made online verbal insult a criminal offence.
Authorities in the UAE last month warned that sending a middle finger emoji symbol would also be punishable under the law.
Swearing at someone via WhatsApp in the UAE could land you with a $68,000 (Â£45,000) fine, under a new law.