The five minute mobile phone film shows 35-year-old Miroslava Prillerova romping with teenager Karel Kucera while his pal with the camera gives the couple instructions.
Furious parents at her school in Znojmo, southern Czech Republic, are demanding her sacking.
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But headmaster Miroslav Krivanek told the Austrian Times: “I cannot sack her because she has not broken any regulations.”
“The boy she had sex with is not underage and this was something she did out of school in her own time. I cannot sack someone for doing what they want,” he added.
Prillerova, who has been on sick leave since the steamy video was seen by thousands, said: “It was New Year’s Eve and Karel and I had had a lot to drink. I just lost control of myself.”
The video has since received millions of views on multiple pornography sites.