Merkel, 59, fell during a cross-country skiing at the resort of Engadin on the foothills of the Swiss Alps and sustained "severe bruise linked to a partial fracture on the left, rear part of the pelvic ring", a government spokesman said.
Initially, it was presumed that she had a painful bruise, but medical examination last Friday showed a fracture of the pelvis bone.
The Chancellor did not require a hospitalisation and has been advised by her doctors to take bed rest at least for three weeks, the spokesman told a news conference.
However, several official engagements scheduled for the coming weeks, including a visit to Poland, the first foreign trip of her third term and a meeting in Berlin with Luxembourg's new prime minister Xavier Bettel have been cancelled.
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The spokesman did not say when the accident occurred.
"She fell down during a cross-country skiing. We believe it was at a slow speed," he said.
Merkel had returned to Berlin from her holiday at the end of December and she delivered her New Year's address on December 30.
Merkel will carry out a major part of her official work in the coming weeks from her residence, where she is recuperating, the spokesman said.
A meeting of her Christian Democratic Union's (CDU) management board scheduled for later this week has been cancelled.