Police said the arrest on Rivelin Valley Road had been made following a complaint about the horn-blowing from a member of the public.
She was arrested for on suspicion of causing intentional harm or distress, under Section 4a of the Public Order Act 1986 and has received a court summons.
A video posted online of the incident shows the woman telling a police officer she had set off the alarm “because they are raping the trees”. Shortly after switching it off and then blowing a horn, she was arrested by police.
The woman said on the video: “I’m not breaking any laws. It’s after seven in the morning and before seven in the evening.”
She said the tree fellers working at the same time with chainsaws were “making more noise than I am”.
There were two others arrests linked to the increasingly-bitter dispute today. A 49-year-old man was arrested for a public order offence after swearing at police officers and received a fixed penalty notice.
A 65-year-old man was arrested on suspicion of obstructing the highway and was also reported on summons.
In another incident, a campaigner was hurt shortly after being removed from inside safety barriers by private security guards working for Sheffield Council contractor Amey.
A spokeswoman for South Yorkshire Police said the woman was lying on the ground outside the safety barriers and was hurt as security guards removed another protester. An ambulance was called and she was taken to hospital.
South Yorkshire Police said the incident had been reported to the force by a third party but it had not received a formal complaint from the person involved.
Clashes between private security guards hired by Sheffield Council contractor Amey and campaigners earlier this year led to a decision to increase the number of officers being sent to tree-felling operations, with dozens being deployed on an almost daily basis.
There have been 14 arrests since the higher policing presence was introduced four weeks ago, with allegations including assault and criminal damage.
One person has been charged with wilful obstruction of the highway in relation to an incident earlier this week.
Separately, eight people have been reported on summons under Section 303 of the Highways Act 1980 and one person has been reported for summons for Aggravated Trespass.
Thousands of street trees in the city are being felled and replaced with saplings as part of a PFI highways maintenance contractor, with campaigners objecting to what they say is the unnecessary removal of healthy trees.
Three MPs in the city have called for the work to be halted so talks can take place following the recent arrests.