Rudiger, 28, was struck during the second half of Chelsea's 2-0 victory as goals from Hakim Ziyech and Thiago Silva gave them their first league win since December 26.
The incident came a day after Aston Villa pair Lucas Digne, who joined from Everton two weeks ago, and Matty Cash were hit by objects thrown by home supporters at Goodison Park.
Merseyside Police have charged a 19-year-old with assault and throwing an item on the pitch during Everton's 1-0 defeat.
" ... Everybody needs to show respect and behave to certain guidelines, there's no doubt about it," said Tuchel.
"If this is a new trend we need to act together to make sure that it stops as soon as possible, to protect the fantastic environment and unique atmosphere of England."
Sky Sports reported Metropolitan Police had made two arrests and were working to identify anyone else involved in throwing objects during the match.