Officers say a man was seen in possession of a large pole on St Ledgers Court at around 5.30pm.
The man was then seen to threaten another member of the public with this pole, waving it around, making attempts to strike the person.
Investigating officer PC Sophia Matthews, based at Milton Keynes police station, said: “I am appealing for anybody who believes that they witnessed this incident, or who may have dash-cam or CCTV footage to please contact Thames Valley Police, either online or by calling 101, quoting reference number 43220221255.
“Alternatively, you can also call the independent charity Crimestoppers anonymously on 0800 555 111.”
A 33-year-old man from Milton Keynes has been arrested on suspicion of affray and possessing an offensive weapon in a public place.
He has since been released on bail until 18 June.
Two days previously, on Friday, There was another incident in Great Linford involving police.
A TVP spokesman said cryptically at the time: “Police have been investigating an incident today today involving a blue tent close to the Co-op local shop, Great Linford Milton Keynes and would like to thank the public for their patience and co-operation.
He said witnesses to the tent incident should call 101 and quote 1257 of 20/5/22.
It is not know if the two incidents were connected in any way.
Last month the same local centre in St Ledger Drive was the scene of a stabbing.
A man aged in his late teens was slashed in the stomach by an masked man outside the Co-op store.