The virus has been detected on one major ward, but test results from patients have come back as negative.
Naas Hospital says a Covid-19 outbreak has been confirmed on one ward, believed to be a 31 bed unit.
The ward is now closed to new admissions.
The hospital says as of last night, there are no confirmed cases there, and 8 suspected cases.
An Outbreak Control Team has been undertaking testing and contact tracing.
Swab results for patients have come back negative, while staff who are close contacts are self-isolating.
It's understood the source of the outbreak could be part of the cleaning team, who tested positive.
Testing at the facility has now been carried out after a risk assessment, according to the HSE.
Over 300 cases have been confirmed in Kildare in the past two weeks.