Carterannounced on Sunday that she is taking a break from social media for the remainder of the tournament.
The 27-year-old has participated in all four of England's matches in the tournament but faced challenges during their quarter-final victory over Sweden on Thursday as the Lionesses allowed two goals in the first half.
Football Association CEO Mark Bullingham denounced the abuse and stated that the FA has been in communication with UK police, who are liaising with the relevant social media platform to "ensure those accountable for this hate crime face justice."
"We support Jess. We support every player and every individual who has experienced racist abuse. No player should face discrimination in any form; they should be free to perform at their best on the field," Infantino remarked in a statement.
"In this case, we will provide our assistance with any necessary actions, as well as share information for suitable measures to be taken against any offenders."
European football's governing body UEFA, Carter's club Gotham FC, the National Women's Soccer League, and the Lionesses also released statements supporting the player.
Carter's teammate Lotte Wubben-Moy stated in an Instagram post that she intends to step away from social media as well.