Bitcoin has been on a wild ride this year. It started out the year at $1,000 and soared above $19,000 on the Coinbase exchange last week before dropping. The price on Coinbase, which accounts for a third of bitcoin trading value, is often at a premium over other exchanges.
"It's a contagion. People are getting excited watching other people [invest]," Shiller said in an interview with "Closing Bell."
"Smart people do invest in it but they're careful. They don't do too much," the Yale University professor said. However, for some people their care is "going by the wayside."
Bitcoin was trading at $17,270 on Coinbase at 4:01 p.m. New York time on Monday.
Shiller, who has called bitcoin a "fad," believes it is OK to "play" with the cryptocurrency.
However, "it would be wrong to put a high percentage of your portfolio in it because it may have gone up tenfold already but that's not guaranteed."
Meltem Demirors, director of development at The Digital Currency Group, is bullish on bitcoin long term.
"We are just getting started and this financial speculation is fueling the development of infrastructure," she told "Closing Bell."
Demirors sees a "much bigger run coming in 2018 when more products and more instruments come to market."