The 37 fish – worth around £8,000 – were stolen from a garden on Honeycross Road in Hemel Hempstead overnight on Thursday (April 21).
Electrical equipment was also taken.
Detective Constable Nia Hadly, from the Dacorum Local Crime Unit, said: “Understandably, the victim is very upset and we’re keen to trace those responsible for the theft as soon as possible.
She added: “We’re appealing for anyone who witnessed any suspicious activity in the area, or who may have captured any CCTV of note, to please come forward.”
The police have said that they are keen to hear from anyone who has across Koi carp being advertised for sale in suspicious circumstances.
Anyone with information is asked to email DC Hadly at [email protected]
You can also report information online or call 101, quoting crime reference 41/31570/22.
Alternatively, you can stay anonymous by contacting Crimestoppers on 0800 555111.