It said the injuries "are not serious", but a "short observation" was required. It gave no further details.
Czech police said they were not investigating the accident because it happened on a closed racing circuit - not on the road.
Mr Pavel, aged 62, is known for his love of motorbikes. He is believed to be currently racing a BMW R1200 GS.
It is not the first time he has attracted trouble over his hobby.
Last year, he had to publicly apologise after being spotted riding a bike without a helmet.
A former high-ranking Nato general, Mr Pavel was elected as the Czech Republic's president in March 2023.
A few weeks after his inauguration, he rode a motorbike to the state of Bavaria in neighbouring Germany.
"The sun, the wind at your back and the strengthening of neighbourly relations with your Bavarian friends. Why not combine the pleasant with the useful," Mr Pavel wrote in a post on X.
Thursday's accident is the latest extra-curricular injury the Czech leader has suffered. In April, he suffered an injury while firing a weapon at a shooting range.
The former general suffered a minor laceration near his eyebrows while shooting with a rifle equipped with an optic, his office said at the time.
DN