Hospices of Hope, which only opened on Mount Pleasant just before lockdown began, was targeted on Thursday [July 2].
It is the third time one of its shops has been attacked by vandals.
Kent Police say over the past month windows have also been deliberately broken at stores run by the Hospices of Hope charity in Tonbridge and near Sevenoaks.
In the latest incident on Mount Pleasant, several front and side windows were shattered.
Officers believe the damage may be linked to previous offences at other locations. Between June 28 and June 29 , windows were broken at a Hospices of Hope shop in Tonbridge High Street, while on 9 June a branch in Otford High Street was also damaged.
The charity has also reported damage to shops in Faversham and in areas outside of Kent, including Bexley and Pimlico in central London.
Hospices of Hope raises money to provide hospice care in Eastern Europe.
Inspector Dave Higham, of the Tunbridge Wells Community Safety Unit, said: “These offences have cost the charity around £30,000 to repair.
“We are keeping an open mind as to whether all of these incidents are linked and the possible motive and urging anyone who may have seen anything suspicious to contact us. We are also asking nearby businesses, some of which may have recently been closed during the Covid-19 restrictions, to check their CCTV systems.”
If you have any information which may assist the investigation call Kent Police on 01622 604100, quoting reference 46/111918/20. You can also contact Kent Crimestoppers, anonymously on 0800 555111 or by using the online form at crimestoppers-uk.org