After the financial crisis, skittish investors flocked to the perceived safety of bonds, despite incredibly low interest rates stemming from the Federal Reserve's aggressive monetary measures to stimulate the economy.
Earlier this year, interest rates jumped sending bond prices tumbling after Federal Reserve Chairman Ben Bernanke suggested that the central bank may begin to scale back its aggressive bond-buying program.
The Pimco Total Return Fund, one of the world's largest bond funds, saw its assets decline by about 12 percent year-to-date through August as a result of losses and investor redemptions, according to Morningstar, an investment research firm.
Financial advisors say that many individual investors—particularly the large numbers of older, income-oriented Americans heavily invested in bonds—are in for a rude awakening if rates continue to rise. With the exception of a few short-term spikes, interest rates have generally declined during the past 30 years, lulling many investors into a false sense of security, advisors say.
"Consumers have never experienced a sustained rising-rate environment, and they generally don't realize what happens to bond prices in that kind of environment," said Ric Edelman, chief executive officer of Edelman Financial Services.
Not all advisors, however, are alarmed at the prospect of somewhat higher interest rates.
In recent years, the low-rate environment has helped to spur economic growth and created a wave of mortgage refinances. However, retirees and other conservative investors have been turned off by paltry yields on CDs as well as Treasurys and corporate bonds, said Barry Glassman, president of Glassman Wealth Services.
"If the rate on Treasurys and corporate bonds were to climb to 4 or 5 percent, many retired people would love this," Glassman said. "That might, in fact, save many retirement plans."
Still, many advisors are taking steps to minimize risk on the fixed income side of existing portfolios by reducing exposure to long-term bonds in favor of those with shorter maturities and/or higher credit quality.
(Read more: Fossil fuels in your portfolio?)
Other advisors are seeking to hedge portfolios against rising interest rates by shifting money from fixed-rate holdings into floating-rate notes with yields tied to benchmarks.
"On the fixed income side, we have dialed down maturities and dialed up credit quality," Cortazzo said. "We are buying shorter-maturity bonds and increasing exposure to high-quality bonds in that space in order to reduce credit risk."
Fearing that other municipalities could follow in the footsteps of bankrupt Detroit, advisors are also becoming much more selective when it comes to municipal bonds, long perceived by investors as one of the safest types of bonds.