Why this move in the yen is so darn scary

The rally in the yen doesn't appear to be stopping anytime soon and its unrelenting strength has traders worried it could quash a struggling Japanese economy.

"Markets are really questioning Japan's ability to stimulate their economy going forward," said Chris Gaffney, president of EverBank World Markets.

The world's third-largest economy expanded at an annualized 1.9 percent rate in the first quarter, a fragile recovery from the fourth quarter's contraction at an annualized 1.1 percent rate. And a strong yen will continue to weigh on growth in the export-driven economy.

On Thursday, the Japanese currency hit 103.58 yen against the U.S. dollar, the strongest level since August 2014.

Concerns around a Brexit were a factor Thursday behind the yen's strength against the dollar, but analysts said the Bank of Japan's inaction overnight was a key driver. The central bank disappointed many by not adding stimulus in light of recent yen strength and added to existing concerns about the effectiveness of monetary policy in helping the economy grow.

"If we broke 100 on a Brexit story I think that would be good cover for the Bank of Japan to intervene to the extent they could say, 'Look we're getting caught up in the backwash of some international event and are getting hit particularly hard.' They could justify it on the back of that," said Alan Ruskin, head of G-10 FX strategy at Deutsche Bank. The Brexit is the U.K. referendum on whether to leave the European Union.

"I'm quite skeptical intervention would be successful," Ruskin said.

The Bank of Japan surprised markets in late January by cutting its benchmark interest rate to negative territory. The historic move was an effort to stimulate the economy and should have weakened the yen against the dollar. But in the days afterward, the Japanese currency strengthened against the greenback.

BOJ Governor Haruhiko Kuroda said at a news conference after Thursday's decision that monetary policy "doesn't target exchange rates" but that the yen's rise "could have undesirable effects on Japan's economy and future inflation."

"I think absolutely central bank credibility will continue to be questioned no matter what happens with Brexit," Gaffney said.

CNBC's Patti Domm and Reuters contributed to this report.