At first glance it seems to be a joke about Angela Merkel, but it is not. If one reads the text as it is, one will be bemused what it is about und why it should be funny. More important, the story about its origin is missing completely.
choXer's answer has explained it, but let me fill in some essential details.
Alice Weidel (co-chairperson of the AfD parliamentary group) was asked if she can tell a joke. She said "no", and the interviewer replied "I give you a "startup" - Kommt die Kanzlerin zum Arzt". After a while Alice Weidel shakes her head and says "no, please help me, what is the continuation?" and the interviewer answers: "Sagt der Arzt: Oh, hier ist es aber dreckig, ich glaube, ich brauche eine Putzfrau, die schwarz arbeitet." As a reaction Alice Weidel laughs and says "that works".
Without the AfD-context
Kommt die Kanzlerin zum Arzt. Sagt der Arzt: Oh, hier ist es aber dreckig, ich glaube, ich brauche eine Putzfrau, die schwarz arbeitet.
would not be funny. The beginning "Kommt die Kanzlerin zum Arzt. Sagt der Arzt:" does not fit at all to what the doctor says. But if you watch the whole video you will notice that in the preceding interview Beatrix von Storch (also AfD) was also asked to tell a joke and she replied "Also ich mal einen Witz: Die Kanzlerin ist noch immer nicht zurückgetreten. Das ist doch eigentlich ganz schön witzig, oder?" I conclude that the interviewer took this up and passed the ball to Weidel to provoke her to say something denigrative about Angela Merkel. Weidel didn't use this opportunity, instead the interviewer stroke a heavy blow by continuing with "Oh, hier ist es aber dreckig, ich glaube, ich brauche eine Putzfrau, die schwarz arbeitet." This refers to Weidel's cleaning lady who was a Syrian asylum seeker. In my opinion that is the main point of the joke, but of course also illegal employment plays a role to point to "Goodie Two Shoes"-behavior of AfD-members.