The said man in the video believed to be the sacked Minister of General Education was seen fondling himself while on live WhatsApp video with a woman in Zambia.
The video of him has been circulating on social media, sparking debates among Zambians.
Mabumba is currently in quarantine over the coronavirus pandemic, according to local media.
Local media reported that police are now investigating the circulation of the nude video with a government official urging the public to stop circulating the video.
Mr Mabumba previously served as energy minister and has now been replaced at the ministry of education by Dennis Wanchinga.
He has not commented on the s3x videos as well as his dismissal on Wednesday.
It was earlier reported by some news portals that he had committed suicide but that has been denied by some of his relatives.