One thousand handmade sunflowers were unveiled in Poole Park earlier this month, each representing someone cared for at Forest Holme Hospice.
A spokeswoman said 12 had been "aggressively smashed to pieces" sometime on Sunday.
Dorset Police confirmed it was looking into a report of criminal damage.
The appeal, inspired by the 2014 ceramic poppy memorial at the Tower of London, encouraged families to buy a sunflower with the name of a relative who stayed at the hospice.
The hospice spokeswoman added: "This was a heartless and needless act which is not only upsetting for those who have dedicated a flower to a loved one, but will also result in a financial loss of Â£300 for our charity."
Supporters have since started an online fundraising effort to recoup the losses.
Sammy Reeves, 26, who set up an online collection, said she was "so angry" after hearing news of the vandalism.
"It's not just the time and effort in setting up the sunflowers, but it creates a lot of hurt and upset - it's just vile."
A memorial to people cared for at a Dorset hospice has been vandalised a fortnight after it opened.