Flores is sidelined with a sore tight lower back and Ramos is battling rotator cuff tendinitis, manager Mickey Callaway said.
In other moves Monday, catcher Kevin Plawecki and reliever Hansel Robles were activated from the DL, outfielder Phillip Evans was recalled from Triple-A Las Vegas and catcher Tomas Nido was optioned to Double-A Binghamton.
Flores left Sunday's 8-7 loss to the Milwaukee Brewers before the bottom of the fourth inning with lower back soreness. He is hitting .248 with three home runs and 13 RBIs.
Ramos was sent back to New York on Sunday after he had allowed eight runs in his past 4⅔ innings pitched. His ERA has ballooned to 6.41.
Plawecki last played on April 11 and has been sidelined with a broken hand. He was hitting .150 at the time of his injury.
Robles went on the DL earlier this month with a sprained right knee. He is 2-1 with a 5.23 ERA this season.