The Ministry of Health did not name the centre and did not specify whether those affected were children or adults but it said the outbreak was localised.
Zimbabwe today recorded 61 new coronavirus cases with 14 of them in Bulawayo.
There were only 19 recoveries resulting in the number of active cases rising to 807.
Harare still has 390 cases followed by Masvingo with 132, Matebeleland South with 79, Bulawayo 68 and the Midlands 55.
Mashonaland Central and Mashonaland East have only six cases, each.
There were five deaths, four of them in Bulawayo.
Deaths have now risen to 1 605, cases to 39 092 and recoveries to 36 680.
Today only 1 922 got their first jab to bring the total to 684 164 while 6 368 completed their course to raise the total of those fully vaccinated to 364 340.