The blaze, believed to be suspicious, took place at around 10pm on Sunday at some stable blocks off Guide Lane.
Fire crews brought the blaze under control but it caused significant damage and resulted in the death of four dogs as well as other small animals.
Det. Sgt Zoe Russo, from Burnley CID, said: “This was a shocking crime which saw a number of animals suffer needlessly to their deaths and thousands of pounds worth of damage. The owner is devastated.
“I am asking anyone who knows anything about this fire to get in contact with us at their earliest opportunity.”
Anyone with information can call Burnley CID on 01282 472118. Alternatively they can ring 101 quoting incident reference 1705 of August 23rd.
Crimestoppers can be contacted anonymously on 0800 555 111 or online at Crimestoppers-uk.org.