Council contractor Amey said "specially-trained stewards" would remove anyone who wilfully obstructed ongoing work to remove damaged trees as part of a Â£2bn scheme.
The council's Streets Ahead programme has seen a long-running battle between campaigners trying to save trees and workers trying to chop them down.
Streets Ahead spokesman Darren Butt said: “Our first priority is to keep people safe and within the law by reminding them to stay out of the safety zones, so we can complete our work for the benefit of everyone in Sheffield.
“However, from today people who do deliberately obstruct our work on the highway will be removed from the zones. This is a decision which is supported by professional legal advice and follows extensive dialogue with Sheffield City Council and South Yorkshire Police.
“Separately, the council is in the process of preparing further proceedings for contempt of court.
“We welcome safe and peaceful protest at all times, but in the face of continued disrespect for the law, as well as increasing abuse of our professional staff, and lack of consideration for local communities, we feel we have no choice.”
All activity within the safety zones is being filmed to ensure the highest standards are maintained and this footage may be used in evidence.
Since 2012, Amey has been delivering the programme on behalf of Sheffield City Council.
The council says the project has overseen the upgrade of many of the city’s roads and pavements.
A council spokesman added: "However, despite our best efforts to carry out the council’s legal duty to maintain the city’s highways, and a High Court injunction to keep our working areas safe, a small minority of people who disagree with the replacement of street trees continue to deliberately obstruct us."
"From today our specially trained stewarding team will take steps to remove people from within the safety zones around our work who try to wilfully obstruct our legal works on the highway and refuse to leave when asked."
As part of Streets Ahead about 5,500 trees have been cut down since 2012.
The authority insists those earmarked for felling are either "dangerous, dead, diseased, dying, damaging or discriminatory".
However, campaigners claim many of the trees classed by the council as "damaging" or "discriminatory" are healthy specimens which should not be cut down.
The council has said every tree will be replaced on a one for one basis and extra trees planted over the contract period.