Dyson's ex, Alexis Blackburn, is accusing the former Minnesota Twins pitcher of flying into a rage and smashing up their cat's play box while the cat was still inside.

Blackburn posted a message on social media -- written in the voice of her cat -- saying, "Someone I trusted with my safety, protection, and love did the unthinkable while I was inside the box."

Blackburn says she moved the cat out of their home -- and says (in her cat's voice), "I don’t have to worry about getting hurt because of anger or control."

"I don’t have to be scared of yelling and things being hurled at mom and me. I don’t have to be scared anymore."

In ANOTHER cryptic post -- using her own voice -- Blackburn alludes to an abusive situation with an unnamed person ... and says, "I am broken."

"I’ve allowed my physical health, my emotional health, and my mental health to diminish to nothing."

A source close to the situation confirmed to The Athletic ... both social media posts were written about Dyson.

An MLB spokesperson tells TMZ Sports, "We are aware of the matter and looking into it."

The Athletic's Ken Rosenthal says MLB is calling the matter a "domestic violence investigation."

So far, no comment from Dyson's camp.

31-year-old Dyson is currently a free agent after spending last season with the San Francisco Giants and Minnesota Twins.