The proposed 50-bed unit on an air force base in central Kenya for Americans exposed to the virus in Democratic Republic of Congo or Uganda has angered many Kenyans.
They accuse the US of offloading the health risk of caring for patients.
A Kenyan court temporarily suspended the plan in response to a lawsuit from a legal advocacy group.
However, US military aircraft have continued to fly in staff and equipment in recent days.
Kenyan High Court Judge Patricia Nyaundi on Tuesday issued an order barring the Kenyan government from taking any steps to build or begin operations at the facility in the town of Nanyuki before the case is resolved.
She scheduled the next hearing for June 23.
The US State Department did not immediately respond to a request for comment.
Hundreds protested against the plan in Nanyuki on Monday.
Protest organiser Patrick Wahome said two people were killed by gunshot wounds after police opened fire.
A security source also said two people had died but did not specify cause of death.
Police spokesman Michael Muchiri said he was not aware of the deaths.
Kenya President William Ruto said the facility was part of a wider national preparedness plan and long-running health partnership with Washington.
Ruto said it would serve Kenyans and foreign nationals too, though US officials have not confirmed this.
"We are a responsible government. We know what we are doing," Ruto said on Monday.
The outbreak of the rare Bundibugyo strain of Ebola is centred in eastern Congo and several cases have spilled over into neighbouring Uganda.
There have been more than 900 suspected cases, including over 220 suspected deaths from the disease.
Experts say the outbreak, declared on May 15, is likely significantly larger and more advanced than official figures suggest after circulating undetected for many weeks.
President Donald Trump's administration has said it "cannot and will not allow" any cases to enter the US, unlike during the 2014-16 Ebola outbreak in West Africa when several infected US nationals were treated on US soil.
A US citizen who contracted Ebola while treating patients in the DRC as a medical missionary was moved to Germany in May for treatment along with five others who were exposed.
A seventh person was taken to the Czech Republic.
The facility in Nanyuki is meant to receive Americans who have been exposed to the virus but are still asymptomatic.
Patients who develop symptoms would be sent for care in other countries, US officials have said.
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