In a statement, Johnson said he was tested for the coronavirus after he began feeling ill late Monday and canceled his Tuesday schedule.
He said his wife, Nikki, who also is fully vaccinated, tested negative for the coronavirus.
Johnson said he had canceled his engagements for the rest of the week. He also said he had notified his recent contacts and the school attended by his sons, who are not yet eligible for vaccination.
“I appreciate your thoughts and prayers on behalf of my family, and I look forward to a speedy recovery so I can get back to work with my colleagues on behalf of the people of Dallas,” Johnson said. “In addition, I want to take this opportunity to again encourage residents of Dallas to get vaccinated if they have not yet done so — and to receive a booster shot when they are eligible. The vaccines have saved lives and can make breakthrough cases, like mine, far less severe.”