Near-zero yields on safe havens continue to feed municipal bond mutual funds.

The dynamic that ferried cash out of money market funds and into municipal mutual funds last year is still playing out. While the pace at which money is fleeing short-term money funds for municipal mutual funds has slowed, it remains ­robust.

Investors shuttled $6.39 billion out of tax-free money market funds during the week ended Feb. 10, according to the Investment Company Institute.

They have withdrawn $24 billion in the past five weeks, and $108.9 billion since the beginning of 2009. The industry has shrunk from more than $500 billion at the beginning of last year to $380 billion, according to ICI.

What is driving this exodus? Many money fund managers agree on the impetus: low yields.

“Low absolute yields in the very front end of the municipal curve” are encouraging investors to take their money into longer-term bonds, the municipal team at BlackRock wrote in a report Friday.

Money funds are required to invest in supremely safe and liquid paper to offer investors the equivalent of cash.

Because of a sharp decline in issuance of the types of products these funds invest in, as well as the Federal Reserve’s campaign to keep interest rates tethered to zero, money funds are having trouble finding paper with any significant yield.

According to iMoneyNet, tax-free money funds yield just 0.02%, a record low.

In her monthly commentary, Deborah Cunningham, executive vice president of Federated Investors, wrote the “bottoming process” in cash yields is moving at a “glacial pace.”

The Fed has not yet offered a hint of raising its target for interest rates, Cunningham said, and yields have picked up only on the very short end of the curve.

Where is the money going?

John Hallacy, municipal strategist at Bank of America Merrill Lynch, wrote in a report on Friday that “at least some of this outflow is finding its way to the longer funds.”

Municipal bond mutual funds reported $69 billion in new money from investors last year, according to ICI, and this year have already attracted about $6 billion more.

Muni funds that report their figures weekly posted a net inflow of $701.2 million for the week ended Feb. 10, according to Lipper FMI.

All municipal funds, including those that report their figures monthly, have reported an average of $1.22 billion in new money a week for the past four weeks.

While this is well below the nearly $2.9 billion average achieved in October, it would have been a record before 2008.

The industry now manages $475.5 billion, the highest total in its history.

Municipal bond mutual funds have returned about 1.1% to investors so far this year, according to a Lipper index tracking the sector’s performance. The sector delivered returns of 19% in 2009.

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