The 21-year-old Polish goalkeeper has been reminded by the club of his responsibilities when using the social network site, and apologised for any offence his remarks may have caused.
Szczesny wrote on Twitter: "I'm sorry if anyone was offended by my previous tweets. There are some thing (sic) we should not joke about and I have crossed the line. Sorry!"
The statements mocking Wales captain Ramsey have since been deleted from Szczesny's timeline.
Ramsey, 21, had posted a picture of himself attending a golf event, to which Szczesny replied: "I don't wanna be rude mate but you look like a rapist on that picture! lol", before following it up with "Looking like a rapist/pedofile (sic) isn't a good thing either ;)"
Ramsey had taken the comments as light-hearted, replying: "jealousy is not a good thing mate" and "I try my best mate we're not all blessed with a good fashion sense like you".
