Paceman Ollie Robinson is to skip Sussex's two games on Friday and Saturday to spend time with his family "after a difficult week", the county announced on Thursday.
The 27-year-old is suspended from playing for England due to historical racist and sexist tweets surfacing when he made his Test debut last week against New Zealand.
Despite the controversy, he impressed with ball and bat in the match, which finished in a draw on Sunday.
He remains suspended from international duty pending the outcome of an investigation into the tweets made in 2012 and 2013.
Sussex, though, offered him their full support, saying they would not be adding to the "significant penalties" he has already suffered.
Instead the club said it would "turn its attention to supporting Ollie in his commitment to continue to educate himself in the area of equality, diversity and inclusion".
"Ollie Robinson will not be part of the Sussex Sharks squad for the team's opening two Vitality Blast fixtures against Gloucestershire and Hampshire Hawks on Friday and Saturday evenings," read the Sussex statement.
"After a difficult week, Ollie has decided to take a short break from the game to spend time with his young family.
"Player and staff welfare -- including mental health and wellbeing -- is a priority for the club and, as such, Sussex Cricket fully supports Ollie in his decision."
Robinson's suspension has divided opinion, with British Prime Minister Boris Johnson and Culture Secretary Oliver Dowden saying the England and Wales Cricket Board's decision was "over the top".
Sussex said Robinson was a very different person to the young man who had made those tweets and he has received the support of all of his team-mates since he returned from the England camp.
They said his tweets are unacceptable but he will be welcomed back when he feels he is in the right frame of mind to resume his season.
"Ollie is a very different man from the one that wrote those tweets and has clearly learned much in the intervening years," read the statement.
"He has made clear the shame, embarrassment, and remorse he feels for the discriminatory comments he made.
"We remain in close contact with Ollie from a welfare perspective and will issue further updates on his availability at the relevant times."