Visits to Ipswich and Colchester hospitals could be suspended if the number of patients admitted with coronavirus starts to rise.
Giles Thorpe, chief nurse at East Suffolk and North Essex NHS Foundation Trust (ESNEFT), said current visiting rules are "under constant review" amid fears over the Omicron variant.
ESNEFT currently allows patients to have one visitor for an hour each day after they have been in hospital for at least 24 hours.
Visits must also be pre-booked with ward teams in advance.
ESNEFT had 63 patients in hospital with Covid as of November 30, with the number steadily falling over recent weeks.
Mr Thorpe said: "The plea from me and our ward teams is to please stick to the rules and for just one person to visit their loved one on the ward where they are being cared for.
"While a patient is on a ward, we can safely monitor their condition and manage the risk of infections being brought into a ward environment by limiting the number of visitors they have and overall footfall to the ward.
"If patients are out and about, it makes that job much more difficult. Please remember that, and all the people we’re caring for, when coming to our hospitals.
"We know how much patients and their loved ones value visiting and we understand that the ongoing restrictions are difficult. That’s why we were keen to reintroduce some visiting as safely and as quickly as possible following the recent trust wide suspension, but we now need everyone’s help to keep visiting open.
"Our visiting policy is under constant review. If we start to see another rise in Covid-19 hospital admissions, we will have no choice but to suspend visiting again, which we do not want to do, but we all have our part to play in preventing the spread of the virus in our hospitals so we can keep visiting going."
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