Johnston, 58, was being evaluated by doctors Thursday morning, but company spokeswoman Kathryn Caulfield declined to comment on his condition. The heart attack occurred late Wednesday afternoon.
"The thoughts and support of our entire company are with Jerry and his family at this time," Robert W. Matschullat, presiding director of the company's board of directors, said in a statement.
Johnston joined the Oakland-based consumer products firm in 1981 and was named CEO in July 2003 after serving as its president and chief operating officer, according to the company's Web site.
Clorox, whose products include Clorox brand bleaches, generated $4.4 billion in revenues in the 2005 fiscal year.
Its shares rose 3 cents to $61.52 in morning trading on the New York Stock Exchange. Its shares have traded in a 52-week range of $52.50 to $66.04.