Police officers were called to Carlton-in-Lindrick shortly after 6.15pm on Monday evening when a man was seen acting aggressively – first in Rotherham Baulk and then Chichester Walk.
A vehicle was then followed a short distance to Harworth before a wider search of the area was undertaken.
A 39-year-old man was later arrested at around 7.15pm on suspicion of affray and has since been released on bail.
A small axe was also found in Chichester Walk and taken away as evidence as investigations continue.
Inspector Susan Wain, of Nottinghamshire Police, said: “This was an alarming incident for people to witness and generated a very swift response from officers.
“Nottinghamshire Police will not tolerate the display of dangerous weapons in public and we worked hard in this instance to track down and arrest a suspect very quickly.
“Investigations are still ongoing and house-to-house enquiries have also been completed. However we are still very keen to speak to anyone else who may have witnessed this incident.
“Anyone with information is asked to call 101 quoting incident 623 of 30 August.”