On Monday a boy of eight was bitten whilst swimming in the Rhine at Lindli, his father told newspaper 20 Minuten.
The animal – which was spotted by the man from the shore – bit the boy twice, once on the shoulder and once on the bottom.
Later the same evening a woman was bitten on the leg so badly she needed to go to hospital to have stitches.
Though she didn’t see the animal and did not know at first how she had been hurt, the injuries she suffered were consistent with the bite wounds visible on the boy.
After the attacks, Schaffhausen authorities told 20 Minuten they intend to erect warning signs to draw attention to the potential danger in the water.
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Such attacks are unusual, local gamekeeper Andreas Vögeli told the paper.
Beavers are only likely to become aggressive if they feel threatened or are defending their nest.
Bathers are advised to avoid swimming close to the shore, and to not allow dogs to enter the water.
Beavers were hunted to extinction around 200 years ago but were reintroduced to Switzerland in the late 1950s.
They have been a protected species here since 1962.
There are now an estimated 2,800 beavers in the country.