Analysts at Bank of Tokyo Mitsubishi explained that this dollar demand would likely outweigh the negative impact on the US dollar from a more dovish outlook for Fed policy.

Key Quotes:

"If Brexit happens, then the Fed will become even more cautious on when to resume gradual rate hikes.

Heightened uncertainty over the outlook for global growth could mean the Fed is side-lined for the remainder of the year.

For Fed policy to have more of a negative impact on the US dollar, we believe that the market would have to believe that the Fed was likely to perform a policy “U-turn” and begin to ease policy.

The Fed would have to become more fearful that the US economy was heading into recession. We doubt that will be the market’s initial Brexit reaction."