Dart last worked on Nov. 19 and received confirmation that he tested positive for the virus on Nov. 24, the release said.
He began feeling symptomatic on Nov. 20 and immediately self-quarantined, the office said.
"The Sheriff is uncertain where he contracted the virus but has been working around the clock to combat the virus at the Sheriff's Office," the release said.
Dart remains symptomatic and is under the care of his physician, officials said.