"It is suspected that Schallenberg might have been infected at the Foreign Affairs Council in Luxembourg on Monday," the spokeswoman said, adding that he did not have symptoms and had been tested as a routine measure.
Wilmes said on Saturday she had tested positive for Covid-19, a day after going into self-isolation with suspected symptoms of the illness.
"Contamination probably occurred within my family circle given the precautions taken outside my home," she said on Twitter, without saying when she might have become infected.
German Foreign Minister Heiko Maas tested negative on Friday and had no close contact with Schallenberg, his ministry said, while Swedish Foreign Minister Ann Linde will work from home until she receives a negative test result, her department said.
French Foreign Minister Jean-Yves Le Drian tested negative on Thursday while on a trip to Algeria.
Schallenberg's only bilateral meeting in Luxembourg was with his Irish counterpart Simon Coveney but social distancing measures were implemented and Ireland has been informed of his positive test, his ministry's spokeswoman said.
Schallenberg also attended a cabinet meeting on Wednesday but cabinet members wore face masks, she added.
"As a precautionary measure all members of the government will be tested on Saturday," the spokeswoman said.
Austria's cabinet had a scare less than two weeks ago when a close colleague of Chancellor Sebastian Kurz's was confirmed to have the virus.
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