Yes: Saudi Post (SPL) describes it as compulsory for every entity in the Kingdom, and several government e-services require it, including those of the Ministry of Commerce. It is SPL's addressing system: a 4-digit building number, a street, a 4-digit secondary number, a district, a 5-digit postal code and a city. A "short address" of 4 letters and 4 digits sums it up.
For a business, the service is called "approved business address" (عنوان الأعمال المعتمد). It requires a commercial registration and an SPL Online account. SPL's published annual fees: SAR 1,000 for a company on its main registration, SAR 300 per branch registration, SAR 500 and SAR 100 for a sole establishment. New businesses are exempt for the first year, and SPL states that its prices may change without notice.
The national address also matters for invoicing. ZATCA's e-invoicing standard (rules BR-KSA-09 and BR-KSA-37) requires the seller's full address on every invoice, with street, 4-digit building number, postal code, city and district, and points to the national address system. A business-centre address entered wrongly gets invoices rejected: see our guide to e-invoicing in Saudi Arabia.