The authority will stop sending press releases to the publication, and Barton and his colleagues will not give interviews or invite them to council events.
Reporters from Nottinghamshire Live and the LDRS will continue to attend public meetings.
A spokesperson for the council said: "The ban, which will only be lifted for emergency scenarios like flooding and weather-related cases, incidents at council-run schools, adult social care, or public safety issues, has come into immediate effect."