Employers created only 18,000 jobs last month, a fraction of what economists expected. Hiring in April and May was weaker than earlier estimates.
Traders rushed to the relative safety of government bonds. The yield on the 10-year Treasury note fell to 3.04 percent from 3.19 percent just before the Labor Department's report came out.
Shortly after the opening bell, the Dow Jones industrial average is down 87 points, or 0.7 percent, at 12,633. The S&P 500 index is down 10, or 0.7 percent at 1,344. The Nasdaq composite index is down 29, or 1 percent, at 2,844.