No, I don't think so that there is any connection to World War II. Moreover not all Jews left the country - my family lives in Germany for several hundred years - and not every Jew fits the stereotype of being "funny", I hope you know that. Moreover there are Jewish comedians in Germany (search for Oliver Polak and Hugo Egon Balder, for example).
In my eyes, the reason why comedy in general is not very popular in Germany lays in society's values. Comedy, a lot of TV et cetera are not considered to be sophisticated and society view people that watch things like that a lot/all the time, are less intelligent. Germans are people that love Theatre and Opera and they read a lot but they are not the ones who watch TV while having breakfast or lunch (that's considered "anti-social") which is "normal" in many American families. This does not mean that there is no comedy - there is, "trash" TV is full of it and you can watch it for hours if you like, but they show it only in the late evening because it is not what the majority likes to watch (as it is considered "cheap"). But I do not think that it has something to do with the war, because as well before the war, Germans were not comedy people but always loved Theatre and things like that - so it is simply a cultural thing and those values are transmitted by society and mainly by education (schools, universities).
)