Esposito portrays Detective Jackie Curatola, Danny Reagan's (Donnie Wahlberg) partner, on the show, which also stars Tom Selleck and Bridget Moynahan.
CBS told Deadline in a statement: "Jennifer has informed us that she is only available to work on a very limited part-time schedule. As a result, she's unable to perform the demands of her role and we regretfully had to put her character on a leave of absence."
After CBS released the news, Esposito, who is battling with coeliac disease, blasted at the network for its "shameful behaviour".
"CBS PUT me on unpaid leave and has blocked me from working anywhere else after my doctor said you needed a reduced schedule due to Celiac," the actress posted on Twitter. "CBS didn't listen to my doc and I collapsed on set. Which everyone saw!
"After a week off, my doc said I could return to work but CBS implied that I was NOT truly ill and this was a scheme to get a raise! It's been almost two months without bringing me back to work + keeping Me from working anywhere else!... Absolutely shameful behaviour."
While Esposito has filmed her last episode for the time being, which will be aired on Friday, November 2, CBS stated that it hopes "that she will be able to return at some point in the future".
The network has cast guest stars to play Reagan's temporary partner, including Megan Ketch.
Blue Bloods airs on Fridays at 10pm ET on CBS.
Watch a video of Blue Bloods's third season below: