Continuous rain throughout the afternoon prompted the decision around 2 1/2 hours before the scheduled pitch first at 7:05 p.m. The forecast called for additional rain well into the evening.
The game will not be made up.
New York will break camp after Tuesday's home game against Detroit. The Rays have two more games, including a spring finale Wednesday against Toronto at Tropicana Field.
The Yankees were busy off the field, making a number of roster decisions.
In addition to the expected move of Eric Chavez earning a spot as the backup to third baseman Alex Rodriguez and first baseman Mark Teixeira, rookie catchers Jesus Montero and Austin Romine lost out in the backup catcher competition.
"When you look at those two young guys, we consider them front-line catchers in the majors someday," Yankees manager Joe Girardi said. "They seem to understand it and will go down with the right attitude. We want them to play everyday. We want, when they come up, not to have to go back."
Gustavo Molina, who has played in 23 major-league games, will be the backup catcher unless the Yankees make a late addition from outside the organization.
Eduardo Nunez beat out Pena for the other reserve infield spot.
Mark Prior, looking to make a comeback with New York after not pitching in the majors since 2006, will remain in Florida to continue his development into a reliever.
"Just because of the weather and the first time he's ever relieved," Girardi said. "Eventually, you want to get where he can give you more than one inning. The weather is much more predictable here. It's warmer for a guy that's never had somewhat of a time limit when he warms up."
Prior went 18-6 with a 2.43 ERA in 30 starts for the NL Central champion Chicago Cubs in 2003.
"They're thinking long term," Prior said. "I think I'm major league ready stuff-wise. I've got to go back to back games. Pitch more than one inning. I know there's a lot of things I can improve on."
Tampa Bay manager Joe Maddon said his roster is fairly set, but isn't ruling out the possibility of a change -- particularly in the bullpen -- before Friday's opener against Baltimore.
"The pitchers look to be set, and they kind of are, but there's still the threat of something else happening," Maddon said.
James Shields, the Rays' scheduled starter, will throw at Tropicana Field on Tuesday. The right-hander will throw 30 pitches instead of the 60 he would have made against the Yankees.
New York's A.J. Burnett threw a simulated game in a batting cage.
The Yankees also released INF Ronnie Belliard and assigned INF Doug Bernier to Scranton/Wilkes-Barre. ... The Rays returned LHP Cesar Cabral to the Boston Red Sox for $25,000. He was selected in the major league phase of the Rule 5 draft last December. Tampa Bay has 26 players in camp, including LHP J.P.Howell, who'll start the season on the disabled list. ... New York is working on a deal to sell the rights of RHP Romulo Sanchez to a Japanese league team.