Officers said the man was suspected of posting a message on Facebook falsely claiming he had left poison on roadsides.
They said they believe the suspect, who is a student, made the alleged threat after reading about a kitten being killed by a Shiba Inu at the Hong Kong Pet Show on Sunday.
The man later deleted the post, police said, after people criticised him for the comment.
Police said they seized two phones and a laptop when they arrested the man who lives in Kwai Chung.
The arrest was made on Thursday, and police said he was still being detained.
The force warned that posting messages that threaten public danger can be a nuisance offence, punishable by up to seven years in prison.
Police stressed that there was no evidence to suggest that any poison had actually been placed on the streets, but said they would carry out further investigation.
They also said they were still looking into the death of the cat at the pet show and whether any animal cruelty was involved.