Singh was to visit Mongolia next month.
"The home minster's visit has been postponed," a ministry spokesperson said.
Singh had suffered the fracture during a morning walk at his residence on June 18.
The visit was aimed at cementing bilateral ties between the two countries.
Prime Minister Narendra Modi had in 2015 visited Mongolia. A Mongolian delegation, led by Deputy Prime Minister Khurelsukh Ukhna, had met the Union home minister in November last year.
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