Sixteen shoppers were injured at the Sweden-based furniture store's showroom in the Red Sea city of Jiddah on Wednesday.
Medics revived some 20 customers who had fainted in the crush.
The stampede was triggered by an offer for the first 50 shoppers to received $150 vouchers.
An official at Ikea's Saudi agent said more than 70,000 people showed up at the Jidda branch.
Hospital officials said the three dead included a Pakistani and a Saudi national.
Ikea is known for simple, reasonably priced products.