Mass testing is currently taking place at the prison, which also has a young offenders institute, with 80 confirmed cases as of yesterday.
The confirmed cases currently centre around blocks HB1 and 6A.
Visiting to anyone who has a confirmed or suspected case of Covid or anyone who is located in an "outbreak area" is currently suspended, as are court hearings from the prison over video link.
Prisoners who also have a confirmed case or self-isolating with symptoms while awaiting the results of a test are not allowed to leave their cells, even for a shower or exercise.
A prison spokesman said: "Following a rise in Covid cases among staff and men, it has been necessary to review how we facilitate access to showers and exercise. Whilst numbers remain high, the following regimes will apply.
"Any man who is confirmed as being Covid positive, or anyone located in an area which has more than six confirmed Covid cases, will operate an 'outbreak regime'. This will mean men will have access to showers and exercise on alternating days Monday to Thursday. Between Friday and Sunday, men will receive one shower and one period of exercise. To ensure everyone gets this regime, you may be offered the regime in the evening during the week.
"On all other units, men will continue to have access to showers and exercise every day Monday to Thursday and for two sessions between Friday and Sunday.
"Any men who display Covid symptoms will be required to fully isolate in their cell pending the result of a Covid test and will not have access to showers and exercise during this period.
"Men confirmed as having Covid, awaiting a test result or located in a Covid area will have meals and medication delivered to their cells. All other men will continue to collect medication and meals as normal, in their regime groups.
The prison is currently providing updates on its Twitter page.
A recent post states: "We know the current situation is worrying for everyone living and working at Moorland and families, but we're working hard with our health providers and Public Health England UK to limit the spread of Covid and keep everyone safe.
"We appreciate all the patience and understanding everyone is showing."