"The Greatest Showman" star took to Instagram on Wednesday, July 10 to share a snap of the vehicle - which was plastered with an image of the 42-year-old and the slogan "Driver does not carry cash, just Aviation Gin" - being removed from its location.
"Couldn't have happened to a nicer guy," Hugh, 50, humorously captioned the picture.
The "Pokemon Detective Pikachu" star later saw the post, and commented with an amusing defence: "What? I have a very elaborate designated driver."
Aviation Gin also chimed in to the conversation, jokingly adding: "We're dedicated to all Aviation Gin personnel having paid time off to relax from the hard work we're doing every day...even the trucks."
The stars are renowned for joking with one another online, after Ryan declared "war" on the "Logan" actor when he wouldn't agree to reprise his role as Wolverine for a future "Deadpool" movie.
"I'm gonna have to step up my game... I'm just gonna just post his cell phone number online!" Ryan joked in an interview with "Good Morning America" last year.