Institutional money will likely be heading for the exits in June, Joe Terranova of Virtus Investment Partners said Monday.

"The question becomes for a money manager, what do you want to buy right here? Do you want to buy cyclicals when the growth really isn't evident? Do you want to buy defensives when you have rising interest rates? I think we're in a period here of 30 days of frustration and exiting from risk assets," he said.

Stocks were mixed in morning trading, with the holding modest gains, the S&P 500 struggling and the declining. The CBOE Volatility Index traded above 16.

(Read More: Stocks Waver After Weak Data)

On CNBC's "Fast Money," Terranova said that it was important to see what institutional investors would do next.

"I already think the month of June is going to be a month where the institutional money is going to a month where the institutional money is looking for exits, whether it's in fixed income, whether it's in equities," he said.

(Read More: Jeremy Siegel Still Sees Dow 17,000 in 2013)

Rosecliff Capital's Mike Murphy noted that large-cap stocks such as Verizon and AT&Twere struggling.

"The action there hasn't been good," he said, pointing out stronger names such as Inteland Hewlett-Packard.

"I think right now what you need to look for as we head into the month of June is companies that haven't peaked out or had too much of a high run, companies where you can see a back-half rally, and I think Intel plays into that this morning."

(Read More: Stocks, Sectors to Watch in June)

OptionMonster's Jon Najarian said that there was no reason to expect the Federal Reserve's backstop would disappear anytime soon.

(Read More: Apple Stock Price Bottom May Be In)

"I'm still in the camp that says the market is not strong enough, the economy's not strong enough to see any significant tapering, so we can talk about the market we want or the market we've got," he said.

Trader disclosure: On June 3, 2013, the following stocks and commodities mentioned or intended to be mentioned on CNBC's "Fast Money" were owned by the "Fast Money" traders: Mike Murphy is long FB; Mike Murphy is long F; Joe Terranova is long VRTS; Joe Terranova is long SJM; Joe Terranova is long AAPL; Joe Terranova is long SPLK; Joe Terranova is long GLD; Joe Terranova is long TBT; Joe Terranova is long SWN; Joe Terranova is long GOOG JUNE 870 PUTS; Joe Terranova is long GS JUNE 165 PUTS; Joe Terranova is short MINI S&P FUTURES; Stephanie Link is long AAPL; Stephanie Link is long GS; Stephanie Link is long JPM; Stephanie Link is long WFC; Stephanie Link is long CSCO; Stephanie Link is long FB ; Stephanie Link is long EBAY; Stephanie Link is long F.