Page told employees in an email on Thursday that there was "nothing seriously wrong with me," according to a source who had seen an internal staff memo.
The 39-year-old Google co-founder sat out his company's annual shareholders' meeting on Thursday because he had "lost his voice," according to Google Executive Chairman Eric Schmidt, who informed attendees of the news at the start of the event.
The condition will also cause Page to miss Google's annual developer conference next week as well as its quarterly results announcement next month.
Page continues to run Google's business, but has been asked to rest his voice, according to a Google spokeswoman. The company declined further comment on his condition.
The prolonged absence from the public spotlight raises questions about his condition, and the company's obligation to disclose issues of concern to shareholders.
Corporate governance experts say Google has met minimal disclosure requirements but will face increasing pressure while Page remains out of sight.
On Friday, Google's shares rose 1.1 percent to $571.48, lifted along with the rest of the Nasdaq.
"It gets them over the first disclosure hurdle, that is they've alerted shareholders to the fact he's going to have this health effect," said James Post, a professor of management at Boston University who specializes in corporate governance issues. "The tough questions still lie ahead, and there will be continued pressure to keep answering those tough questions."
While many people, including senior business executives, prefer to keep health matters private, public company CEOs have responsibilities to a "wide set of constituents, some of whom have a legitimate claim to know about material information," said Post.
The issue came to the fore several years ago when Apple was criticized for being less than forthright about the health of CEO Steve Jobs, who died in October after a long struggle with pancreatic cancer.
"With the concerns over Steve Jobs, people are quick to jump to a conclusion that may not be the right conclusion to jump to," said Needham & company analyst Kerry Rice.
Page's health could be regarded as an especially significant issue because he, along with Schmidt and co-founder Sergey Brin, have majority control of the Internet company through special voting shares.
Wall Street analysts mostly took the news of Page's extended absence in stride, though some expressed concern about the lack of information.
"It's the number one thing I'm concerned about today just because there's so little data available," said BGC Partners analyst Colin Gillis.
JP Morgan analyst Doug Anmuth noted that Page has not posted any messages to his Google+ profile since May 25.
"We have no specific reason to think there is anything more to Larry's condition, but we find it odd that the company would already rule him out of the 2Q call, which is likely still a few weeks away," Anmuth wrote to clients late on Thursday.
"This could raise some questions among investors."
Simon Best, a head and neck surgery specialist at the Johns Hopkins Voice Center, said most cases where a doctor might order a patient to rest their voice involved either a vocal chord hemorrhage, or throat surgery of some sort.
"We actually very rarely put people on complete voice rest where they are not cleared to talk or allowed to talk," West said. "There are probably some practice differences between physicians and whoever is treating him, but there are only two scenarios where we put people on voice rest: if they've had vocal cord surgery, or if they've had a vocal chord hemorrhage."
Best, who has not treated Page, said hemorrhages were easily treatable, but a wide variety of conditions might necessitate surgery.
The Wall Street Journal first reported on the details of Page's internal memo on Friday.
During the shareholder meeting on Thursday, Google's Schmidt tried to lighten the situation by relaying comments that co-founder Brin had made about Page's condition: Sergey "has said that this problem will make Larry a better CEO because he's going to have to choose his words very carefully."
copyright @ Thomson-Reuters 2012