A statement this evening confirmed the latest swabs had highlighted another four infections within the squad.
They have been placed into self-isolation and the local health authorities informed.
There were already five who had tested positive, but one of those turned negative today and will now have a medical examination before he can be allowed to resume training.
Venezia have not named any of the individual players who have been infected with COVID-19.
The cut-off point for a Serie A match to potentially be postponed is nine players who simultaneously are positive for the Coronavirus.
That is 35 per cent of a 25-man squad.
Venezia are currently at eight and their next match will be against Napoli on February 6 at the Stadio Penzo.
Meanwhile, Cristiano Biraghi had a temperature and was placed into self-isolation during the Italy get-together pending the results of a COVID-19 test.
Fiorentina already have Dusan Vlahovic, Riccardo Saponara and Lucas Torreira testing positive.