How Long Does It Take the Invisalign Aligners to Arrive?

Align technologies does try to keep the wait to around 4 weeks, but sometimes the wait is much longer. If the case is complicated, the number of aligners to create can be large, which would add to the wait time.
You should call the dental office and ask. They might have an idea what the status is and what kind of wait is left.

I'm going to cross post my answer... The number of trays fabricated has very little to do with the time taken to ship... Most of the time, Align Tech is waiting for instructions from the doctor...
Impressions are shipped via UPS with 2-3 day shipping to California where the impressions are processed. Photos and radiographs emailed to Align Technology may take a few days to be matched to the delivered impressions.
Your models are then turned into a simulation in Costa Rica. It takes a few days to construct the ClinCheck and for your orthodontist to receive their first simulation of your teeth. Depending on the movements shown, your orthodontist may require making revisions to idealize your treatment. Since simulations are made by techs rather than orthodontists, it is important that your provider spend adequate time designing your treatment and revising it as necessary. It may take a day or two for a new simulation after each revision. Techs also work on Saturdays while your orthodontist may not be looking to plan your treatment on weekends. Premier and Elite providers have their own dedicated technician who may be more familiar with specific treatment goals.
Your orthodontist may ask you to come in to view the treatment outcome prior to fabrication of the trays. Upon acceptance of your case, aligners may take a few days to make depending on the volume at the factory in Mexico. Other practices may choose to provide the simulation to you after fabrication.
Aligners are then shipped via 2-3 day UPS back to your orthodontist's office in North America. There may be longer times in other parts of the world.
The total time required depends on the above factors. Assuming no revisions or prefabrication consultation, the aligners could theoretically be ready in about 2.5-3 weeks. We tend to schedule our patients 5-6 weeks after the initial impression. If aligners arrive earlier, we contact our patients if they would like to begin treatment ahead of their originally scheduled appointment as most are eager to begin treatment!