The incident occurred on Tuesday in the tourist resort of Nanyuki at the air base that houses the facility.
The 50-bed quarantine center will accommodate Americans arriving from Congo-Kinshasa, the epicenter of the ongoing Ebola outbreak. Kenya has no recorded cases of the virus, and the construction has sparked anger over the risk of the dangerous disease entering the country.
The protesters set fires and threw stones at the police, who responded with tear gas and water cannons. There was also gunfire and, according to the AFP news agency, one man was hit in the head.
Dozens of people were arrested by the police.
