Carter’s England team-mate Lotte Wubben-Moy said she would be also be coming off social media.
UK Prime Minister Sir Keir Starmer said: “There is no place for racism in football or anywhere in society.
“I stand with Jess, the Lionesses, and any players who have suffered racism, on and off the pitch.”
Carter, who made her England debut in 2017 and has 49 caps, was a member of the squad that won Euro 2022.
Having started her career at Birmingham City, she won five Women’s Super League titles with Chelsea before leaving for American club Gotham FC last summer.
The United States National Women’s Soccer League side said they were “heartbroken and outraged”.
“Jess is not only a world-class football player, she is a role model, a leader and a valued part of our Gotham FC family,” the club said.
“We stand with Jess, and we deeply appreciate the support for Jess from the Lionesses and England’s Football Association.”
Anti-discrimination charity Kick It Out sent its support to Carter, and backed her decision to step away from social media.
Kick It Out said those responsible “should face the strongest possible consequences”, adding “responsibility also lies with social media companies”.
It said: “We have been working with the government and the regulator, but we know that more urgency is needed from everyone involved.”
Uefa, European football’s governing body Uefa, said: “Abuse and discrimination should never be tolerated, whether in football or society, in person or online.”
The Lionesses’ next match is against Italy in the Euro 2025 semi-finals on Tuesday.