Pompeo slammed Fleiss for his comments about Ripa, who hosts Live! with Kelly and Ryan on ABC, the same network as The Bachelor.
"Okay @fleissmeister... that's some handle bro! Your show does NOT pay @KellyRipa salary. Also we don't attack successful women on our network and men certainly cannot take credit for their success. Don't get me started on your show cuz I'm a savage.... #bachelorsoooowhite," Pompeo wrote.
Ripa discussed The Bachelor during Tuesday's episode of her show, saying the reality competition "disgusts" her.
"I can't stand the idea of 25 exceptional women fighting over one ordinary fella, in my opinion," she said. "You know how I feel, ladies, we are too special to be arguing over a guy."
Fleiss responded to Ripa's remarks in a tweet Tuesday.
"Easy, @KellyRipa ... #TheBachelor franchise pays your salary!" he wrote.
Pompeo plays Meredith Grey on Grey's Anatomy, which airs its Season 15 finale Thursday. The actress discussed the show's future in an interview with USA Today in February, saying she never takes anything for granted.