This little guy has been circulating around the internet today, claiming he's an alien from Star Trek. Do we know if that's true? And what episode of ToS is he from? What is he?
This is from "The Enemy Within", episode 5 of season 1 of Star Trek: The Original Series. The creature is never named in the episode, although the planet they found it on is stated to be Alpha 177, so Memory Alpha calls it the "Alfa 177 Canine".
Here's a screenshot from the same episode with Kirk holding the same creature:
Technically, your screenshot shows the evil twin of the creature Kirk is holding. The whole premise of this episode is a transporter malfunction that splits this creature and then Kirk into good and evil twins.
The scene that your screenshot probably comes from was transcribed by chakoteya as follows:
KIRK: What is it, Scotty?
SCOTT: Transporter breakdown. Continue circuit testing. We beamed up this animal and, well, look for yourself. It's in this specimen case. (opens lid to reveal angry pink animal)
SCOTT: A few seconds after they sent this one up through the transporter, that duplicate appeared. Except it's not a duplicate, it's an opposite. Two of the same animal, but different. One gentle, this. One mean and fierce, that. Some kind of savage, ferocious opposite. Captain, we don't dare send Mister Sulu and the landing party up. If this should happen to a man.
KIRK: Oh, my.
This wonderful creature is known as the "Alfa 177 Canine", seen in the Star Trek: TOS Episode The Enemy Within.
More information can be found on Memory Alpha at the following link: Alfa 177 Canine