The videos reportedly involve high-ranking civil servant Baltasar Ebang Engonga having sex with various women - including the wives of prominent officials - in his office.
Mr Engonga is head of the country's National Financial Investigation Agency and also a relative of the country's president.
He has not yet commented.
Vice-President Teodoro Obiang Mangue said any officials found engaging in sex acts at work would be suspended as this was a "flagrant violation of the code of conduct".
He has also ordered the installation of surveillance cameras in courts and ministries to combat "indecent and illicit acts".
A statement from the vice-president's office said the decision had been taken in the wake of the widely circulated videos which had "denigrated the image of the country".
It added that he had recommended opening an investigation.
The videos in question were leaked after Mr Engonga was arrested on separate corruption charges, state television TVGE said.
Last week, Vice-President Obiang said "pornographic videos" had been "flooding" social media and ordered telecoms companies to curb the spread.
Since then, the flow of internet traffic - particularly the downloading of images - has been severely disrupted in the country, people in Equatorial Guinea told the AFP news agency.
As head of the National Financial Investigation Agency, Mr Engonga works on tackling financial crimes such as money laundering.
Following the furore over the videos, Equatorial Guinea's chief prosecutor Anatolio Nzang Nguema told state TV that if Mr Engonga was found to have been "infected with a sexually transmitted disease" he would be prosecuted for an offence against "public health".
He is reportedly nicknamed "Bello" - Spanish for beautiful - on account of his good looks.
๐ฎ๐๐๐๐๐๐บ๐ ๐ต๐๐ฝ๐พ๐ ๐๐๐ฝ๐พ๐ ๐๐๐๐ ๐๐๐พ ๐๐๐๐พ๐๐๐พ๐ ๐ป๐ ๐๐๐๐๐ ๐บ๐๐ฝ ๐บ๐๐บ๐๐พ๐ฝ ๐๐๐พ๐๐พ๐๐ ๐๐ ๐๐บ๐๐๐๐๐ ๐๐๐ผ๐๐บ๐ ๐๐พ๐ฝ๐๐บ ๐๐ ๐บ๐๐ฟ๐๐๐๐ All ๐๐๐๐บ๐ ๐ฟ๐๐ ๐ ๐๐๐ฝ๐พ๐ ๐ ๐พ๐บ๐๐พ๐ฝ ๐๐๐ผ๐๐บ๐ ๐๐พ๐ฝ๐๐บ ๐๐๐๐๐๐พ๐
๐ฎ๐๐๐๐๐๐บ๐ ๐ต๐๐ฝ๐พ๐ ๐๐๐ฝ๐พ๐ ๐๐๐๐ ๐๐๐พ ๐๐๐๐พ๐๐๐พ๐ ๐ป๐ ๐๐๐๐๐ ๐บ๐๐ฝ ๐บ๐๐บ๐๐พ๐ฝ ๐๐๐พ๐๐พ๐๐ ๐๐ ๐๐บ๐๐๐๐๐ ๐๐๐ผ๐๐บ๐ ๐๐พ๐ฝ๐๐บ ๐๐ ๐บ๐๐ฟ๐๐๐๐ All ๐๐๐๐บ๐ ๐ฟ๐๐ ๐ ๐๐๐ฝ๐พ๐ ๐ ๐พ๐บ๐๐พ๐ฝ ๐๐๐ผ๐๐บ๐ ๐๐พ๐ฝ๐๐บ ๐๐๐๐๐๐พ๐
๐ ๐ข๐ซ๐จ๐ข๐ช ๐ง๐ค๐ฑ๐ค ๐ข==โบโบ ๐ถ๐ ๐ณ๐ข๐ง ๐ญ๐ฎ๐ถ
๐ด ๐ข๐ซ๐จ๐ข๐ช ๐ง๐ค๐ฑ๐ค ๐==โบโบ ๐ฃ๐๐๐๐ ๐๐บ๐ฝ ๐ญ๐๐
๐ด ๐ข๐ซ๐จ๐ข๐ช ๐ง๐ค๐ฑ๐ค ๐==โบโบ ๐ฃ๐๐๐๐ ๐๐บ๐ฝ ๐ญ๐๐
The videos reportedly involve high-ranking civil servant Baltasar Ebang Engonga having sex with various women - including the wives of prominent officials - in his office.
Mr Engonga is head of the country's National Financial Investigation Agency and also a relative of the country's president.
He has not yet commented.
Vice-President Teodoro Obiang Mangue said any officials found engaging in sex acts at work would be suspended as this was a "flagrant violation of the code of conduct".
He has also ordered the installation of surveillance cameras in courts and ministries to combat "indecent and illicit acts".
A statement from the vice-president's office said the decision had been taken in the wake of the widely circulated videos which had "denigrated the image of the country".
It added that he had recommended opening an investigation.
The videos in question were leaked after Mr Engonga was arrested on separate corruption charges, state television TVGE said.
Last week, Vice-President Obiang said "pornographic videos" had been "flooding" social media and ordered telecoms companies to curb the spread.
Since then, the flow of internet traffic - particularly the downloading of images - has been severely disrupted in the country, people in Equatorial Guinea told the AFP news agency.
As head of the National Financial Investigation Agency, Mr Engonga works on tackling financial crimes such as money laundering.
Following the furore over the videos, Equatorial Guinea's chief prosecutor Anatolio Nzang Nguema told state TV that if Mr Engonga was found to have been "infected with a sexually transmitted disease" he would be prosecuted for an offence against "public health".
He is reportedly nicknamed "Bello" - Spanish for beautiful - on account of his good looks.