AMC Entertainment Holdings, the biggest US theatre chain, couldn't handle the traffic when tickets went on sale on Tuesday (Wednesday NZ time).
Fandango, a top ticket supplier, also struggled to meet demand. It put customers in queues, and then told them, "The line is paused".
Disney's Marvel Studios also released a new trailer for the film, helping stoke excitement.
AMC likened the crash to the moment in the previous Avengers movie when villain Thanos kills half the people in the universe.