As a result, "you might want to consider holding your bitcoins on your exchange, so if there's a mass exodus of people rushing for the door, your money will already be on the exchange, so you can sell your bitcoin core coins for more bitcoin cash or whatever else you want," Ver said.

Roger Ver, CEO of Bitcoin.com, said Wednesday on CNBC's " Fast Money " that "bitcoin miners" may shift their processing power over to bitcoin cash if the offshoot becomes popular enough.

An outspoken proponent of the bitcoin offshoot, bitcoin cash, said investors may want to keep their holdings on an exchange right now.

"Whereas if they're stuck on your own phone or your own computer and everybody's running for the door ... it will be too late at that point to move your own bitcoins from your own wallet onto an exchange," he said. "You wind up getting nothing instead of something."

The advice runs contrary, Ver said, to what he told investors for years: not to hold bitcoin on exchanges, which can be hacked. Morgan Stanley analysts estimate more than $630 million in bitcoin has been stolen from cryptocurrency exchanges by hackers, according to a Monday report.

Ver was an early investor in bitcoin and earned the nickname "Bitcoin Jesus." But he has become a bitcoin cash supporter, because he sees the offshoot digital currency as being faster, cheaper and more reliable to use than the original version.

Bitcoin cash split off from bitcoin on Aug. 1 after a minority of developers decided to implement an upgrade to improve transaction efficiency. Leading U.S. cryptocurrency platform Coinbase added trading for bitcoin cash this week, in a rocky rollout that shows the growing pains of the digital currency exchange industry. Bitcoin payments processor BitPay and cryptocurrency storage company Blockchain also added support for bitcoin cash in the last few days.

Bitcoin cash traded about 33 percent higher over the last 24 hours at $3,786 as of 6:03 p.m. Wednesday, according to Coinbase. Bitcoin traded more than 6.5 percent lower, near $16,337, the site showed.

The digital currency has soared about 2,000 percent over the last 12 months on a surge of investor interest. The world's largest futures exchange, CME, launched bitcoin futures Sunday, one week after its competitor Cboe Global Markets began trading its own bitcoin futures. The move is expected to allow institutional investors to buy into the cryptocurrency trend.

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