BlackRock's chief investment officer of fundamental fixed income said on "Squawk Box" the government's May nonfarm payrolls number of 38,000 growth was "extreme," but the trend lower was "real," considering how much the labor market has improved in recent years.
Economists had expected 164,000 new jobs last month.
"We've had pretty extraordinary job hiring," said Rieder, noting that 7.5 million jobs were created in the past three years. "It's more than the prior 13 [years] combined."
The unemployment rate fell to 4.7 percent, a greater-than-expected 0.3-point decline that can be partly explained by a drop in the rate of participation in the labor market. An average hourly earnings gain of 0.2 percent matched estimates.
Investors are looking to Fed Chair Janet Yellen's 12:30 p.m. ET speech on Monday for what this worst jobs report in more than five years means for a possible summer rate hike.
The Fed meets next week, and in late July.
"I think Chair Yellen will keep July open and see. You get a lot of data between now and the ... [July] meeting. You get a couple of CPI reports; you get another payroll report; you get retail sales," Rieder said.
Regardless when another rate increase happens, Rieder said there's room before the economy would be impacted.
"If you move the funds rate to 75 or 100 basis points, it's not going kill the economy," he said. "In fact, we don't think it would even diminish the effects in the economy."
The Fed increased rates for the first time in more than nine years in December — bumping up the fed funds overnight lending rate to a range of 0.25 to 0.5 percent from zero to 0.25 percent.
Central bankers have been watching for continued improvement in jobs and economic growth, while looking for inflation to increase to its 2 percent target.
Rieder said the economy looks pretty good.
"We're coming off the boil. [But] I don't think we're going into a recession," he said. "I think people have to recognize this is going to be a slower growth period."
U.S. gross domestic product advanced at an annual rate of 0.8 percent in the first quarter, according to last month's second estimate from the government. The economy expanded 2.4 percent for all of 2015.
"If you think about what potential growth is in this country, could you trend up to a 3 or just over 3 [percent]? I think that's right," Rieder said.
On inflation, the latest government reading showed a year-on-year increase of 1.1 percent for the consumer price index.