However, the star of Taken did not adapt another of his famous quotes by saying "I will find you and I will eat you," staff joked, according to TMZ.
Neeson stayed long enough to pose for photos with staff but took his meal back to the film set.
The 64-year-old actor is in the city to film Hard Powder, a movie about a snowplow driver seeking revenge against the drug dealers he thinks killed his son.
Staff hope he will return and try a new sandwich they have created in honour of him.
"That's because it has a lot of beef, a one-two punch of bacon and hickory sticks and spice that will get revenge on you tomorrow," Alex Johrden, spokesman for Big Star Sandwich Co, told CBC.
Johrden said they had served a number of film crews in recent years but he was the biggest star they had served.
"This is about the most A-list star we've ever had, but in the area, we've had Elijah Wood and the like," he said.