The girl, from Afghanistan, was living with her family in a centre for asylum seekers in Zweisimmen, in the canton of Bern.
According to a statement by Bern police, the family was due to be deported from Switzerland under the Dublin rules, which state that a person must claim asylum in the first EU country they enter, a policy to which Switzerland adheres.
At around 7am on Wednesday Bern police came to collect the family on the orders of the Swiss migration office, said news agencies.
As she was getting her things together, the 15-year-old opened a window on the first floor and jumped out, falling several metres.
Injured, she was taken to hospital by ambulance.
Speaking to news agencies, a spokesman for Bern police said the family's deportation has been suspended until the girl recovers.
According to the latest figures from the Swiss migration office (SEM), 14,277 asylum applications were made in the first six months of this year, a 20 percent rise on the same period last year.
In June, the SEM refused 585 applications in accordance with Dublin rules, and 778 migrants left the country or were repatriated.