Chelsea submitted a formal complaint to the Premier League that alleged Clattenburg used "inappropriate language" towards two of its players during the Blues' 3-2 defeat to Manchester United in west London.
The alleged comments are understood to have been interpreted as racist.
"If a match official has used racial insults or language to a player then he's for the high jump," Winter told Radio 5 Live.
"He won't be getting a four-match or an eight-match ban, it'll probably be the end of his career, but that is if indeed he did say anything."
Clattenburg was unavailable for comment directly, but the body that represents referees, Professional Game Match Officials (PGMO), has released a statement in which it said the referee has promised to co-operate with any investigation.
Winter feels there is no way that Clattenburg can continue refereeing while the allegations are hanging over him.
"I feel it very unlikely that
Winter admitted that he found it ironic that this time it was a referee that has been accused of using inappropriate language given that officials are subjected to abuse from players and fans at almost every match.
Winter added: "Initially it is insulting words and I must admit I smiled at that because we watch football matches every week of the year hearing players use insulting words to referees and then somebody takes umbrage when somebody allegedly says something back. But I just hope this can be cleared.
"It's slightly ironic that players dish it out left right and centre and then, if and there is a massive if, if something has been said back - and we're not talking about racial here, we're talking about like for like - then I don't think anybody's got a right to complain.
"I'm not saying referees should do it, but there seems to be one law for one set of people and one law for another, but this inference that racial language has been used is very, very serious."
English Premier League
An Edin Dzeko double and a late Micah Richards winner helped Manchester City secure an astonishing 4-3 win over Chelsea in St Louis.