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.
"We want everyone to be able to grab their Avengers: Endgame tickets, but it looks like we've gotten Thanos' snap," the movie chain told customers on Twitter.
Box Office Pro is forecasting opening-weekend sales of US$265 million in North America for Endgame, which opens on April 26 in the US. That would exceed the record US$257.7 million set by its predecessor Infinity War last year.
Box Office Pro also projects US$645 million for the film's full domestic run. That's short of the US$936.7 million record set by another Disney film, Star Wars: The Force Awakens, according to Box Office Mojo.
New Zealand fans will be the first in the world to see the film, which launches here at 10am on April 24.