Kenyans have strongly opposed the plan and deadly protests have taken place since the facility was announced in May for potential US citizens evacuated from the Democratic Republic of Congo, which is grappling with a major Ebola outbreak.
It has been constructed at Laikipia Air Base, about 200 kilometres (125 miles) from the capital, Nairobi, with some 50 isolation beds and was expected to be managed by US medical staff.
Kenya's government ignored a previous order by the high court to stop work on the site.
Rights groups had petitioned the court, saying the facility was being developed secretly and without consultation.
On Monday, the court said health minister Aden Duale was held in contempt for failing to respond to the order and should appear for sentencing.
He appeared in court on Tuesday and apologised, saying: "I have directed the immediate and complete cessation of any intended construction, site preparation, or related activities concerning the Laikipia Air Base facility pending the hearing and determination of the substantive petition or until further orders of this court."
Three people have been killed in unrest near the facility in Laikipia.
Kenya has never recorded a case of Ebola and many oppose bringing potential carriers of the highly contagious disease into the country.
The United States has also pledged $13.5 million to support Kenya's Ebola preparedness efforts, but critics also oppose what they see as colonial overtones in the arrangement.
