The cryptocurrency surged to a record $9,732.76 on Monday, according to coin industry site CoinDesk, breaking a mark set during Thanksgiving weekend. It later retreated to around $9,655 at midmorning.
"Bitcoin has gone parabolic, so that usually doesn't end well," said Cashin, UBS director of floor operations at the New York Stock Exchange.
"I think we're in the fear-of-missing-out phase now," Cashin said in an interview on "Squawk on the Street." "I think initially there was some concern. I am told — and take this with a huge grain of salt — that the movement is even beginning to worry some people in the Federal Reserve."
Cashin says some questioned if bitcoin, which has risen more than 900 percent this year, could be disruptive to currency markets. "It's not quite that big yet," he said. "But certainly its capitalization is moving around."
Bitcoin's price has risen in recent months after the announcement that CME Group would start offering bitcoin futures.
Regarding the overall stock market, Cashin said it isn't in a "celebratory mood" on Monday as investors assess a Senate vote on tax reform expected later this week.
On Monday, President Donald Trump tweeted the "tax cut bill is coming along very well."
"I think they're thinking more consolidation and a slight degree of caution," Cashin said. Congress is back, so we'll see if" they can pass a bill, he said.
Some Wall Street analysts expect "a couple of days or weeks moving sideways," he added. "The Dow looks most susceptible to that."
— CNBC's Evelyn Cheng and Reuters contributed to this report.