Mighty disappeared near the couple’s home in Montecito, California.
The poodle is chipped and his collar has a number to call if found.
Bloom, 43, offers a reward for the safe return of the dog, but the Lord of the Rings star has only asked fans to send “real information.”
He wrote on Instagram to his 4.1 million followers: “MIGHTY IS MISSING in Montecito California.
“He’s chipped and his collar has a number to call – if you take him to your local vet or shelter or police station, he can be traced back to me for a reward.
“Please send only REAL INFORMATION – my heart is already broken, so please do not add insult to injury.” “
There were the best wishes of at least one of the couple’s famous friends.
Danish model Helena Christensen commented on Bloom’s Instagram post: “I can’t imagine the pain you’re going through. Mighty must and will be found. ”
British star Bloom and Perry, 35, who are expecting their first child together, also own another poodle called Nugget.
Nugget and Mighty often appear on celebrity social media accounts.