He and his teammates took a private tour of the museum, which serves as a monument to the nation's struggles in race relations and was also the site of the Lorraine Motel, where an assassin's bullet took the life of Rev. Martin Luther King Jr.
The motel is an integral part of the exhibition.
"The whole thing was kind of surreal," said Sabathia, the Tribe's starter on Opening Day and one of the few black starting pitchers in the Majors today. "It was weird; it was eerie -- very eerie, you know."
He found he couldn't step into the motel portion of the exhibition. He took a glance at it; he wanted to go inside, he said. He simply couldn't will himself to take those steps.
Perhaps the pain of walking where a civil rights icon had lost his life proved too much for Sabathia, an athlete who's shown a willingness to give back to society.
"I called home last night and just talked to my wife about it," he said. "I told her that as soon as my son is old enough to understand that stuff, we're definitely coming back. I think that's something he definitely needs to see."
Sabathia's trip to the museum was structured around the Civil Rights Game, presented by AutoZone. The game itself served as a tribute to the role baseball played as one of the steps toward better relationships between blacks and whites.
No American sport played a bigger role in civil rights and in the lives of blacks than baseball.
Yet the tie between baseball and blacks is a loose one these days. The sport has struggled to keep its foothold in the black community, a point that Sabathia, Commissioner Bud Selig and others stressed during two days of discussions here.
They all talked about how to rejuvenate interest in baseball among black fans, particularly among black youth. Sabathia has been in the forefront of those discussions.
As he had weeks earlier, Sabathia reiterated his concern for the declining number of blacks in baseball, which was a theme that ran through the two days. He pointed to Major League players as having a key role in reviving interest among blacks, but he didn't see even that as any easy answers or a quick fix.
"That Civil Rights Museum is something that every African-American in the country needs to see, because that wasn't that long ago that this stuff was going on," Sabathia said. "It wasn't that long ago, and I think people tend to take things for granted.
"Touring that museum would definitely humble a lot of people."