Hail broke off part of the nose and left cracks in the cockpit windows of the Austrian Airlines aircraft, which was carrying holidaymakers back from Palma de Mallorca.
After issuing a distress call, the plane landed safely at Vienna airport.
None of the passengers or crew were injured in the incident. The airline did not say how many people were on board.
"According to the cockpit crew, the storm was not visible on the weather radar," the airline said in a statement sent to AFP on Monday.
In recent weeks, torrential rains have led to flooding across Austria, with firefighters carrying out more than 2,000 operations in several provinces.
The area close to the border with Slovenia and Hungary in the southern provinces of Styria and Burgenland has been especially hard hit, with a dam reportedly breaching.
Local authorities said Monday they were still searching for a 77-year-old retiree who went missing in Burgenland after driving to the polling station to vote in Sunday's European elections.
In Styria, six polling stations were flooded or rendered inaccessible on Sunday, local officials told AFP.
Over the weekend, a 36-year-old Croat died after the excavator he was operating fell into a stream in Styria late on Friday, police said in a statement, adding they consider his death to be a work accident.
Austria's national weather service warned that rainfall would continue until Wednesday evening.
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