Rieder, who oversees about $1.85 trillion in bond assets for the world's largest money manager, also predicted that the Federal Reserve was getting near the end of raising interest rates. Overall, BlackRock has $6.3 trillion in assets under management.
"I don't think they're going to go that many times next year," he said, calling for one or two rate hikes next year, which is certainly a contrarian point of view. The markets, and even the Fed in its own forecasting, thinks three rate increases are on the docket for 2019.
"The Fed is going to go in December. No doubt," Rieder said. That would make four rate hikes in 2018.
In a "Fast Money Halftime Report" interview, Rieder said he was getting nervous about his 3.25 percent prediction for the 10-year yield by year-end a few months back, when the yield was at 2.75 percent.
"What the Fed is looking at today is some pretty incredible growth that's aided by stimulus that we think could actually start to slow in the next year," he said. "Global growth has been good. But global growth is turning down significantly."
With the economic data starting to show signs that 2019 could see a slower rate of growth, Rieder thinks bond yields are nearing the end of their jump to seven-year highs.
"I'm not that worried about interest rates killing off risk [assets] of any significant magnitude," he said. Stocks could pull back a couple percent, but the longest bull market since World War II appears safe, he added.
On Friday, the 10-year yield settled at 3.23 percent, just off the highest level since May 2011, which it hit earlier in the session. The stock market was slammed last week in the rising yield environment.
The U.S. bond market was closed for Columbus Day on Monday, which was seen as a relief to stock investors who were watching further weakness without the added pressure of trying to figure out where yields were heading.
Last week, Fed Chair Jerome Powell said the central bank still has a ways to go yet before it gets rates to where they are neither restrictive nor accommodative. That stoked concerns about a faster-than-expected rise in the cost of borrowing money.
Projections released after last month's policy meeting indicated central bankers were likely to take the funds rate to 3.4 percent before pausing.