The popular Gauck, 76, who has held the largely ceremonial post of head of state since 2012, made the announcement at Berlin's Bellevue Palace, citing his advanced age.
"I'm grateful to be doing fine," he said, after speculation about health concerns.
"At the same time, I am aware that the life phase between 77 and 82 is a different one than the one I am in now. I cannot guarantee that I would have the same energy and vitality for another five-year term."
His decision not to run for a second mandate complicates the political equation for Merkel, who will have to fill the job just as campaigning for the general election, expected to be held in September 2017, kicks off.
"The search for a successor will start the general election campaign more than 15 months before the poll -- a conflict that the chancellor would have preferred to avoid," news website Spiegel Online said.
"Seldom have we seen someone with his personality in politics. His departure also heralds the end of a generation that shaped Europe's identity," the daily Sueddeutsche Zeitung said.
It added, however, that Germany would do well to seek diversity in its choice for the president, who serves as a kind of moral arbiter for the nation.
"With that in mind, those considering Gauck's successor would do well to look beyond the traditional Christian, ageing grandfatherly types. The office of federal president would emerge the winner if greater consideration were given to the next head of state's gender, religious beliefs or age."
Berlin's Tagesspiegel newspaper said the horsetrading that is expected in backing a candidate for president was "sure to send a signal" about likely coalitions after the general election.
It said that if Merkel's Christian Democrats had to seek the backing of the opposition Greens to win a majority for their pick, it could lay a foundation for an unprecedented coalition between the parties at the national level.
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