Professor uploaded a recommendation meant for university 'A' to a different university 'B'
How it affects you is impossible to say, not knowing nearly enough. 

But it is really the professor's job to make the correction if it is needed as s/he made the error. You can send mail to the program(s) informing them of the error, of course, and they may, individually have some suggestions. But if the mail comes from the professor it would have more weight. The prof can include the proper letter in the mail, of course. 

But if radically different things were said about you (unlikely) it might have an effect. 

But ask your professor to provide the remedy.