Cruz leads the Rangers with 23 home runs and 70 RBIs. He hit a home run in Monday's 3-0 victory over the New York Yankees, the same day Milwaukee Brewers outfielder Ryan Braun accepted a season-ending suspension for his role in the affair.
"I don't know what [Cruz is] going through because I've never been in that situation, but I think he's handled it admirably," Washington said. "He's been a pro, and he has been able to separate what he has done on his job, which is come to the ballpark and play baseball, and what he's done out of here. He's done a good job of separating."
Cruz didn't comment on a possible suspension after Monday's game, saying that he was focusing only on coming to the ballpark and playing baseball.
ESPN investigative reporter T.J. Quinn reported Monday that suspensions for the other players who have been linked to the Miami-area clinic could come down in the next few weeks.
Cruz's teammate Joe Nathan, who was with him at the All-Star Game last week in New York, praised Major League Baseball for "weeding out" those who are using performance-enhancing drugs.
Nathan didn't comment on Cruz's situation because he said he doesn't know anything about it.
Washington said Tuesday that the manager, the coaches and the players will support Cruz.
"We'll embrace him," Washington said. "That's all we do around here is support, and we support Nelson. We can't do anything about his circumstances, but we support him. Until Major League Baseball decides what they want to do, I don't think about it. I'll put his name in my lineup. Until I get word that I can't put it in there, I'll put him in there."
Washington also praised Major League Baseball and the players for wanting to change things in the game, starting with the Braun suspension.
"There's a consequence for your action," Washington said. "He made a mistake; there's a consequence for it. I don't think I have the right to sit here and judge anybody. Major League Baseball I think is doing a fantastic job trying to clear it up. The players have already said that they want it straightened out, and this is one of the consequences for a guy that's a star player, and he has to pay. I think he has to answer that.
"I can't sit here and try to bash him or anything like that. He made a mistake, and Major League Baseball has a penalty for it. He'll pay his penalty, and then he'll be reinstated back into baseball."
Todd Wills covers the Texas Rangers for ESPNDallas.com.