The latest rating was Clinton's first sub-60 percent ranking since 2008, Gallup said.
Clinton's unfavorable rating in June was 39 percent, up from 31 percent in April.
The poll indicates only slight changes in the public's overall assessment of Clinton, the Princeton, N.J., polling agency said.
Although she has said she isn't interested in seeking the Democratic nomination for president in 2016, several media polls indicate she is the front-runner. While she was a popular official in the Obama administration, recent congressional testimony about the attacks on the U.S. Consulate in Benghazi, Libya, called her leadership into question,Gallup said.
Democratic and Republican attitudes toward Clinton have been static, but independents' views were less favorable, with 52 percent of them saying they had a favorable opinion of Clinton, down from 63 percent in April.
Results are based on nationwide telephone interviews of 1,529 adults conducted June 1-4. The margin of error is 3 percentage points.