Ramirez, who started the season with one hit in his first 16 at-bats, was out of the lineup for Wednesday's game against the Los Angeles Angels.
"We talked a little bit and then decided not to play him today," Rays manager Joe Maddon said. "I know it's early in the season, but nevertheless, I think he's still pressing a bit. I really think that he's trying to carry too much of this load right now. He's trying to be too much right now."
Maddon said Ramirez also will miss Thursday's game at the Chicago White Sox while tending to a personal matter.
Ramirez went 0 for 4 with three strikeouts in Tuesday night's 5-3 loss to the Angels.
"With guys like him, I think sometimes we forget, and I mean this in a manner that I hope people understand, it's not easy to be him sometimes," Maddon said. "There's a lot going on with his guy. He will be a Hall of Famer. He's in the latter part of his career. So, you can have different kind of moments mentally.
"I've been around players like that in the past, and I think at some point it just takes a little more understanding for whomever is working with that person. I really believe he's going to very productive in the very near future."
Ramirez said he had no problem with fans booing him after his final couple of at-bats Tuesday.
"It's all right," Ramirez said. "It's not my first time (to strikeout three times). I'm just getting myself out. I feel good. I'm not mad at myself."
Teammates, including ace David Price, feels the boos were not justified.
"I guess they wanted instant results," Price said. "Everybody in here has confidence in Manny. He's going to come around."
Ramirez remains upbeat despite his early struggles, saying that he is not pressing in an attempt to impress anyone.
"I've got almost 600 home runs," Ramirez said, with a smile.