According to the PMI, you’ll receive your certificate package within eight weeks if pass the PMP certification exam.
When I passed my PMP Certification Exam, I was informed immediately via the computer screen that I would receive my certificate package within eight weeks.
I received it in the third week.
In my PMI-RMP test, I saw the message on the screen that I would receive my certificate package within six weeks (but in an e-mail from the PMI, they mentioned I would receive my certificate package within eight weeks; I don’t know the reason for this discrepancy).
Update: I got my PMI-RMP Certificate in less than three weeks.
Though the PMI says that you will receive the certificate within four to eight weeks, in most of the cases I know professionals have received it within four to six weeks. If you do not receive it within eight weeks, you should contact PMI customer care to issue a new certificate.