Mobile testing has now been introduced at the West Calder prison as new figures show that 90 cases of the virus were recorded up to yesterday (Friday).
Six positive cases were first recorded among inmates on 12 February.
The majority of prisoners are self-isolating in their cells to stop further transmission, it is understood.
It comes as official statistics revealed the number of Covid cases in Scotland's prisons has almost doubled in a week.
Official Scottish Prison Service (SPS) figures from Friday 19 February show the total number of cases spiked from 189 to 364, after a major outbreak at HMP Kilmarnock, where 247 positive cases were identified.
Virtual visiting has been suspended at all three prisons in a bid to reduce the spread of the virus.
The SPS said in a statement: "We continue to work closely with public health colleagues in the relevant health boards in managing these cases.
"On the recommendation of the Incident Management Teams, mobile testing units have this week been working in HMP Addiewell, HMP Dumfries, and HMP Kilmarnock to support the prompt identification of cases."
Figures also show 157 staff, 3.5 per cent of the total workforce, are currently absent from their work across Scottish prisons due to reasons related COVID-19. This includes those who are symptomatic, self-isolating, shielding or caring for family members.
The Scottish Government said the wellbeing of prisoners was a priority and that outbreaks were being "well managed".
NHS Lothian were contacted for comment.