The mandate was issued Monday. It was first reported by the Houston Chronicle.
"It is so very important that we remain vigilant in doing our part to reduce the spread of COVID-19," a release from Turner's office read.
The mandate, which goes into effect on Aug. 4, means that all city employees must wear face coverings while on city premises.
This order comes after Gov. Greg Abbott signed an executive order last week, barring mask mandates.
ABC13 asked if the mandate defied the state order. A city spokesperson said, "I don't think so."