Authorities in both countries, whose currencies are pegged to the US dollar, said they were keeping an eye on the impact of the Brexit vote, but that their banks' exposure is limited.
"Due to the limited connection between the UAE financial system and that of the UK, the channels through which financial institutions in the UAE could be affected by the state of uncertainty over relations between the UK and the EU are limited," said the UAE's central bank.
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In a statement carried by the UAE's official WAM news agency, the central bank said it will "continue to watch developments... mainly those that could affect the UAE economy."
The governor of the Saudi Arabian Monetary Agency, Ahmed al-Kholifey, said the OPEC kingpin had already "revised its investment policy regarding assets denominated in euro and sterling pounds" ahead of Thursday's historic vote.
"It is early to assess the impact of the UK exit from the EU... but we expect the impact on the banking sector to be minimal due to its limited exposure to those two currencies," he said, quoted by the official Saudi Press Agency